Abstract This paper analyzes the combined effects of buoyancy force, convective heating, Brownian motion, thermophoresis and magnetic field on stagnation point flow and heat transfer due to nanofluid flow towards a stretching sheet. The governing nonlinear partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations using similarity transformations and then tackled numerically using the Runge–...

Published in 2013]]>Abstract In the present article, two dimensional boundary-layer flows and the heat transfer of a Maxwell fluid past a stretching sheet are studied numerically. The effects of magnetohydrodynamics (MHD) and elasticity on the flow are considered. Moreover, the effects of nanoparticles are also investigated. Similarity transformations are presented to convert the governing nonlinear partial differential equation into coupled ordinary ...

Published in 2013]]>The aim of the present work is to carry out a simplified mathematical modelling for nonlinear stress analysis of plates under temperature changes and mechanical transverse loads. The material properties of the plate are proposed to be temperature-dependent. The geometrically nonlinear plate theory is employed to understand the stress distribution due to thermo-mechanical loads. A set of coupled ...

Journal: Journal of Physics: Conference Series, vol. 382, no. 1, 2012]]>A super heater is a device that is used to convert wet, saturated steam into dry steam. Dry steam at 538oC contains more thermal energy. It increases the overall efficiency of the cycle. The Modelling of the Super heater is done to control the temperature. The paper deals with simulation of control of power plant Super heaters by means of ...

Published in 2012]]>A completely integrable nonlinear partial differential equation (PDE) can be associated with a system of linear PDEs in an auxiliary function whose compatibility requires that the original PDE is satisfied. This associated system is called a Lax pair. Two equivalent representations are presented. The first uses a pair of differential operators which leads to a higher order linear system for ...

Journal: Applicable Analysis, vol. 91, no. 2, pp. 381-402, 2012]]>The exhaustive classification of stationary incompressible flows with constant total pressure of ideal infinitely electrically conducting fluid is given. By introduction of curvilinear coordinates based on streamlines and magnetic lines of the flow, the system of magnetohydrodynamics equations is reduced to a nonlinear vector wave equation extended by the incompressibility condition in a form of a generalized Cauchy integral. For ...

Journal: Journal of Physics A-mathematical and Theoretical - J PHYS A-MATH THEOR, vol. 45, no. 23, 2012]]>Start-up thin film flow of fluids of grade three over a vertical longitudinally oscillating solid wall in a porous medium is investigated. The governing non-linear partial differential equation representing the momentum balance is solved by the Fourier-Galerkin approximation. The effect of the porosity, material constants as well as oscillations on the drainage rate and flow enhancement is ...

Journal: Communications in Nonlinear Science and Numerical Simulation - COMMUN NONLINEAR SCI NUMER SI, vol. 17, pp. 35-44, 2012]]>The option pricing problem when the asset is driven by a stochastic volatility process and in the presence of transaction costs leads to solving a nonlinear partial differential equation (PDE). The nonlinear term in the PDE reflects the presence of transaction costs. Under a particular market completion assumption we derive the nonlinear PDE whose solution may be used to find ...

Journal: Quantitative Finance - QUANT FINANC, vol. 12, no. 4, pp. 663-670, 2012]]>In this study, approximate Green's functions for a vector equation for the electric field with anisotropic dielectric permittivity and magnetic permeability is obtained by means of homotopy perturbation method (HPM). The HPM deforms the nonlinear partial differential equations to a system of manageable partial differential equations. These systems become amenable to analytical solutions which have been expressed in the ...

Journal: Journal of Electromagnetic Waves and Applications - J ELECTROMAGNET WAVE APPLICAT, vol. 26, no. 1, pp. 24-33, 2012]]>The two-dimensional equilibrium with flexible boundaries is solved via using a MAT-LAB Equilibrium Code (MEC), which has applied the finite element method to handle the changeable plasma shape and employed the trust-region dogleg method to solve the nonlinear partial differential equation. The corresponding driven current profile is also calculated by coupling with the lower-hybrid simulation code (...

Journal: Plasma Science & Technology - PLASMA SCI TECHNOL, vol. 14, no. 3, pp. 215-221, 2012]]>Recently, Tian and Friedman et al. developed a mathematical model on brain tumour recurrence after resection [J.P. Tian, A. Friedman, J. Wang and E.A. Chiocca, Modeling the effects of resection, radiation and chemotherapy in glioblastoma, J. Neuro-Oncol. 91(3) (2009), pp. 287–293]. The model is a free boundary problem with a hyperbolic system of nonlinear partial ...

Journal: Applicable Analysis, vol. ahead-of-p, no. ahead-of-p, pp. 1-18, 2012]]>This study considers magnetohydrodynamic flow and heat transfer outside a hollow stretching cylinder immersed in a fluid saturated porous medium of sparse distribution of particles with high permeability. Partial slip boundary conditions for the velocity and temperature fields are assumed at the stretching surface of the cylinder. Using similarity transformations, the nonlinear partial differential equations governing the flow and heat ...

Journal: Numerical Heat Transfer Part A-applications - NUMER HEAT TRANSFER PT A-APPL, vol. 62, no. 2, pp. 136-157, 2012]]>Backward stochastic differential equations (BSDEs) in the sense of Pardoux–Peng [Lecture Notes in Control and Inform. Sci. 176 (1992) 200–217] provide a non-Markovian extension to certain classes of nonlinear partial differential equations; the nonlinearity is expressed in the so-called driver of the BSDE. Our aim is to deal with drivers which have very little regularity in ...

Journal: Annals of Probability - ANN PROBAB, vol. 40, no. 2012, pp. 1715-1758, 2012]]>In this thesis we will explore some interconnections among the following topics: 1. Reﬂectionless potentials; 2. inverse problems in physics; and 3. the solitonic solutions of completely integrable nonlinear partial differential equations. We will begin by discussing the form of the reﬂectionless potential and the nature of solutions of the associated Schrödinger equation. Then we will give an overview of ...

Published in 2012]]>It is significantly important to search for exact soliton solutions to nonlinear partial differential equations (PDEs) of mathematical physics. Transforming nonlinear PDEs into bilinear forms using the Hirota differential operators enables us to apply the Wronskian and Pfaffian techniques to search for exact solutions for a (3+1)-dimensional generalized Kadomtsev-Petviashvili (KP) equation with not only constant coefficients but also ...

Published in 2012]]>The aim of this work is to use the Pfaffian technique, along with the Hirota bilinear method to construct different classes of exact solutions to various of generalized integrable nonlinear partial differential equations. Solitons are among the most beneficial solutions for science and technology, from ocean waves to transmission of information through optical fibers or energy transport along protein molecules. ...

Published in 2012]]>One of the most efficient ways of solving nonlinear partial differential equations is by an algebraic method such as the modified extended tangent hyperbolic function (METF) method aided by symbolic computation. We investigate the proton dynamics of a hydrogen-bonded (HB) chain with an asymmetric double-well potential based on a two-component soliton model. We solve the associated dynamical ...

Journal: Physica Scripta - PHYS SCR, vol. 86, no. 2, 2012]]>In this article, a numerical investigation on a steady two-dimensional mixed convection boundary layer flow along a moving semi-infinite vertical plate is presented. The plate is assumed to move with a constant velocity in the direction of the flow. The influence of internal heat generation or absorption is also included in the analysis. The nonlinear partial differential equations ...

Journal: Chemical Engineering Communications - CHEM ENG COMMUN, vol. 199, no. 5, pp. 658-672, 2012]]>In this paper, the coupled viscous Burgers’ equations have been solved by using the differential quadrature method. Two test problems considered by different researchers have been studied to demonstrate the accuracy and utility of the present method. The numerical results are found to be in good agreement with the exact solutions. The maximum absolute errors L∞ between the exact solutions ...

Journal: International Journal for Computational Methods in Engineering Science and Mechanics, vol. 13, no. 2, pp. 88-92, 2012]]>This paper considers two types of nonlinear partial differential equations, namely the Kaup–Kupershmidt-type (KK-type) equations (KK-I and KK-II), which are of fifth order in space. We propose a Korteweg–de Vries (KdV)-type hierarchy relation and the associated differential operators to show that the KK-type equation can be regarded as a generalization of the ...

Journal: Physica Scripta - PHYS SCR, vol. 85, no. 3, 2012]]>Development of enhanced geothermal systems (EGS) will require creation of a reservoir of sufficient volume to enable commercial-scale heat transfer from the reservoir rocks to the working fluid. A key assumption associated with reservoir creation/stimulation is that sufficient rock volumes can be hydraulically fractured via both tensile and shear failure, and more importantly by reactivation of naturally existing ...

Published in 2012]]>When hadrons scatter at high energies, strong color fields, whose dynamics is described by quantum chromodynamics (QCD), are generated at the interaction point. If one represents these fields in terms of partons (quarks and gluons), the average number densities of the latter saturate at ultrahigh energies. At that point, nonlinear effects become predominant in the dynamical equations. The hadronic states ...

Published in 2012]]>We discuss the class of equations∑i,j=0mAij(u)∂iu∂ti∂u∂tj+∑k,l=0nBkl(u)∂ku∂xk∂u∂xl=C(u)whereAij(u), Bkl(u) and C(u) are functions of u(x,t) as follows: (i) Aij, Bkl and C are polynomials of u; or (ii) Aij, Bkl and C can be reduced to polynomials of u by means of Taylor series for small ...

Journal: Communications in Nonlinear Science and Numerical Simulation - COMMUN NONLINEAR SCI NUMER SI, vol. 16, no. 3, pp. 1176-1185, 2011]]>The similarity solution for the MHD Hiemenz flow against a flat plate with variable wall temperature in a porous medium gives a system of nonlinear partial differential equations. These equations are solved analytically by using a novel analytical method (DTM-Padé technique which is a combination of the differential transform method and the Padé approximation). This method is applied t...

Journal: Computers & Fluids - COMPUT FLUIDS, vol. 40, no. 1, pp. 172-178, 2011]]>We prove a uniqueness theorem in terms of value distribution for meromorphic solutions of a class of nonlinear partial differential equations of first order, which shows that such solutions f are uniquely determined by the zeros and poles of f−cj (counting multiplicities) for two distinct complex numbers c1 and c2.

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 377, no. 2, pp. 881-888, 2011]]>The objective of this work is to manage water flooding of a reservoir to achieve optimal oil production by employing an optimal model-based control framework that uses uncertain parameter updating and a particular reduced-order model. A Markov chain Monte Carlo method is used to update the proposed distributions of the uncer- tain parameters. To avoid excessive simulations of ...

Published in 2011]]>This study investigates the unsteady mixed convection flow past a vertical porous flat plate moving through a binary mixture in the presence of radiative heat transfer and nth-order Arrhenius type of irreversible chemical reaction by taking into account the diffusion-thermal (Dufour) and thermo-diffusion (Soret) effects. Assuming an optically thin radiating fluid and using a local similarity variable, ...

Journal: Chemical Engineering Communications - CHEM ENG COMMUN, vol. 198, no. 7, pp. 920-938, 2011]]>The parametric vibration and stability of the functionally graded ceramic-metal plate subjected to in-plane excitation is presented. Based on the stress–strain relationship and nonlinear geometric equations of nonhomogeneous materials, the nonlinear partial differential equations of this problem were derived by using principle of virtual work. For the simply supported rectangular plate, the displacement function was assumed and ...

Journal: Mechanics Based Design of Structures and Machines - MECH BASED DES STRUCT MECH, vol. 39, no. 3, pp. 367-377, 2011]]>The work presents an analysis of solutions to a free boundary value problem for a multispecies biofilm growth model in one space dimension. The mathematical model consists of a system of nonlinear partial differential equations and a free boundary. It is quite general and can include a large variety of special situations. An existence and uniqueness theorem is discussed and ...

Journal: Mathematical and Computer Modelling - MATH COMPUT MODELLING, vol. 53, no. 9-10, pp. 1596-1606, 2011]]>The exp-function method is applied to a system of nonlinear partial differential equations, and generalized solitary solutions with free parameters are obtained. The solution procedure is simple with the help of symbolic computation.

Journal: Computers & Mathematics With Applications - COMPUT MATH APPL, vol. 61, no. 8, pp. 2081-2084, 2011]]>This paper applies the variational iteration method (VIM) and semi-inverse variational principle to obtain solutions of linear and nonlinear partial differential equations. The nonlinear model is considered from gas dynamics, fluid dynamics and Burgers equation. The linear model is the heat transfer (diffusion) equation. Results show that variational iteration method is a powerful mathematical tool for solving linear and ...

Journal: Applied Mathematics and Computation - AMC, vol. 217, no. 16, pp. 7039-7047, 2011]]>In this paper, a nonlinear size-dependent Euler–Bernoulli beam model is developed based on a strain gradient theory, capable of capturing the size effect. Considering the mid-plane stretching as the source of the nonlinearity in the beam behavior, the governing nonlinear partial differential equation of motion and the corresponding classical and non-classical boundary conditions are determined using ...

Journal: International Journal of Engineering Science - INT J ENG SCI, vol. 49, no. 11, pp. 1256-1267, 2011]]>Unsteady hydromagnetic Generalized Couette flow and heat transfer characteristics of a reactive variable viscosity incompressible electrically conducting third grade fluid in a channel with asymmetric convective cooling at the walls in the presence of uniform transverse magnetic field is studied. It is assumed that the chemical kinetics in the flow system is exothermic and the convective heat transfer at the ...

Journal: Computers & Mathematics With Applications - COMPUT MATH APPL, vol. 61, no. 4, pp. 1167-1179, 2011]]>We introduce non-standard, finite-difference schemes to approximate nonnegative solutions of a weakly hyperbolic (that is, a hyperbolic partial differential equation in which the second-order time-derivative is multiplied by a relatively small positive constant), nonlinear partial differential equation that generalizes the well-known equation of Fisher-KPP from mathematical biology. The methods are consistent of order &...

Journal: International Journal of Computer Mathematics - IJCM, vol. ahead-of-p, no. ahead-of-p, pp. 1-16, 2011]]>The subject of this paper is the development of a general solution procedure for the vibrations (primary resonance and nonlinear natural frequency) of systems with cubic nonlinearities, subjected to nonlinear and time-dependent internal boundary conditions—this is a commonly occurring situation in the vibration analysis of continuous systems with intermediate elements. The equations of motion form a set of ...

Journal: Journal of Sound and Vibration - J SOUND VIB, vol. 330, no. 22, pp. 5382-5400, 2011]]>In this paper we present some methods for solving nonlinear partial differential equations which are based on the idea of the projective Riccati equations. We show how to derive well-known methods such as Conte’s projective Riccati equation method, tanh–coth method, He’s exp-function method and a new method we called sn–ns method. We illustrate the effectiveness of ...

Journal: Computers & Mathematics With Applications - COMPUT MATH APPL, vol. 61, no. 2, pp. 470-481, 2011]]>The first integral method is an efficient method for obtaining exact solutions of some nonlinear partial differential equations. This method can be applied to nonintegrable equations as well as to integrable ones. In this paper, the first integral method is used to construct exact solutions of the nonlinear Schrödinger equation.

Journal: Journal of Mathematical Analysis and Applications - J MATH ANAL APPL, vol. 374, no. 2, pp. 549-553, 2011]]>In this paper, we propose an orientation-matching functional minimization for image denoising and image inpainting. Following the two-step TV-Stokes algorithm (Rahman et al. in Scale space and variational methods in computer vision, pp. 473–482, Springer, Heidelberg, 2007; Tai et al. in Image processing based on partial differential equations, pp. 3–22, Springer, Heidelberg, 2006; Bertalmio et ...

Journal: International Journal of Computer Vision - IJCV, vol. 92, no. 3, pp. 308-324, 2011]]>This paper uses He’s Homotopy Perturbation Method (HPM) to analyze the nonlinear free vibrational behavior of clamped-clamped and clamped-free microbeams considering the effects of rotary inertia and shear deformation. Galerkin’s projection method is used to reduce the governing nonlinear partial differential equation. to a nonlinear ordinary differential equation. HPM is used to find analytic expressions for nonlinear natural ...

Journal: Journal of Mechanical Science and Technology - J MECH SCI TECHNOL, vol. 25, no. 3, pp. 557-565, 2011]]>A synergic duo simulation–optimization approach was developed and implemented to study protein–substrate dynamics and binding kinetics in living organisms. The forward problem is a system of several coupled nonlinear partial differential equations which, with a given set of kinetics and diffusion parameters, can provide not only the commonly used bleached area-averaged time series in fluorescence microscopy experiments ...

Journal: Computers in Biology and Medicine - COMPUT BIOL MED, vol. 41, no. 1, pp. 24-36, 2011]]>In this study, we investigate the transient problem of Generalized Couette flow and heat transfer in a reactive variable viscosity third grade liquid with asymmetric convective cooling. It is assumed that exothermic chemical kinetics takes place in the flow system and the convective heat exchange with the ambient temperature at the channel surface follows Newton’s law of cooling. The coupled ...

Journal: Mathematical and Computer Modelling - MATH COMPUT MODELLING, vol. 54, no. 1, pp. 160-174, 2011]]>The effects of surface slip and heat generation (absorption) on the flow and heat transfer of a non-Newtonian power-law fluid on a continuously moving surface have been examined. The governing nonlinear partial differential equations describing the problem are transformed to nonlinear ordinary differential equations using suitable transformations. The transformed ordinary differential equations are solved numerically using the fourth ...

Journal: Mathematical and Computer Modelling - MATH COMPUT MODELLING, vol. 54, no. 5, pp. 1228-1237, 2011]]>The present work investigates the effects of disks contracting, rotation and heat transfer on the viscous fluid between heated contracting rotating disks. By introducing the Von Kármán type similarity transformations through which we reduced the highly nonlinear partial differential equation to a system of ordinary differential equations. This system of differential equations with appropriate boundary conditions is responsible for th...

Journal: Applied Mathematical Modelling - APPL MATH MODEL, vol. 35, no. 7, pp. 3154-3165, 2011]]>An extended coupled sub-equations expansion method is proposed to seek new traveling wave solutions of the coupled nonlinear partial differential equations. The generalized Schrödinger–Boussinesq and coupled nonlinear Klein–Gordon–Schrödinger equations are used to illustrate the validity and the advantages of this method.

Journal: Applied Mathematics and Computation - AMC, vol. 217, no. 21, pp. 8468-8481, 2011]]>This article deals with the effects of mass transfer on the two-dimensional stagnation point flow of an upper-convected Maxwell (UCM) fluid over a stretching surface. The similarity transformations convert the governing nonlinear partial differential equation into nonlinear ordinary differential equation. Computations for the outcoming systems are presented by a homotopy analysis method (HAM). Graphical results for the velocity ...

Journal: International Journal of Heat and Mass Transfer - INT J HEAT MASS TRANSFER, vol. 54, no. 15, pp. 3777-3782, 2011]]>The method of simplest equation is powerful tool for obtaining exact and approximate solutions of nonlinear PDEs. Here we extend the class of equations which can be treated by the method in such a way that the classes of equations considered in our previous work are particular cases of the extended class of equations. As examples for application of the ...

Journal: Communications in Nonlinear Science and Numerical Simulation - COMMUN NONLINEAR SCI NUMER SI, vol. 16, no. 8, pp. 3033-3044, 2011]]>In this paper, we establish exact solutions for some special nonlinear partial differential equations. The (G′/G)-expansion method is used to construct travelling wave solutions of the two-dimensional sine-Gordon equation, Dodd–Bullough–Mikhailov and Schrödinger–KdV equations, which appear in many fields such as, solid-state physics, nonlinear optics, fluid dynamics, fluid flow, quantum field theory, electromagnetic ...

Journal: Pramana-journal of Physics - PRAMANA-J PHYS, vol. 77, pp. 1-13, 2011]]>In this work, we formulate a Multiobjective Optimization problem using conflicting performance objectives in polymerization systems such as maximize monomer conversion and minimize molecular weight distribution. The problem is subject to a mathematical model comprising highly nonlinear Partial Differential Equations. These describe the dynamic response of the poly(methyl methacrylate) cell-cast process. A full discretization approach was used for ...

Published in 2011]]>In this paper, an efficient algorithm of logarithmic transformation to Hirota bilinear form of the KdV-type bilinear equation is established. In the algorithm, some properties of Hirota operator and logarithmic transformation are successfully applied, which helps to prove that the linear terms of the nonlinear partial differential equation play a crucial role in finding the Hirota bilinear form. Experimented ...

Journal: Applied Mathematics and Computation - AMC, vol. 218, no. 5, pp. 2200-2209, 2011]]>The elliptic Monge-Ampère equation is a fully nonlinear Partial Differential Equation which originated in geometric surface theory, and has been applied in dynamic meteorology, elasticity, geometric optics, image processing and image registration. Solutions can be singular, in which case standard numerical approaches fail.In this article we build a finite difference solver for the Monge-Ampère equation, which converge...

Journal: Journal of Computational Physics - J COMPUT PHYS, vol. 230, pp. 818-834, 2011]]>We study a pointwise control problem for the Boussinesq system in two dimensions. The control is a source term in the heat equation, and the cost functional takes into account the distance between the solution to the Boussinesq system and a given profile. We have recently studied similar problems for the linearized Boussinesq system (Nguyen and Raymond, J. Optim. Theory ...

Journal: Systems & Control Letters - SCL, vol. 60, no. 4, pp. 249-255, 2011]]>In this article, homotopy perturbation method is applied to solve nonlinear parabolic–hyperbolic partial differential equations. Examples of one-dimensional and two-dimensional are presented to show the ability of the method for such equations.

Journal: Journal of King Saud University - Science, vol. 23, no. 1, pp. 99-103, 2011]]>This article examines the thermal effects in an unsteady flow of a pressure driven, reactive, variable viscosity, third-grade fluid through a porous saturated medium with asymmetrical convective boundary conditions. We assume that exothermic chemical reactions take place within the flow system and that the asymmetric convective heat exchange with the ambient at the surfaces follow Newton’s law of cooling. ...

Journal: Computers & Mathematics With Applications - COMPUT MATH APPL, vol. 62, no. 9, pp. 3343-3352, 2011]]>A completely integrable nonlinear partial differential equation (PDE) can be associated with a system of linear PDEs in an auxiliary function whose compatibility requires that the original PDE is satisfied. This associated system is called a Lax pair. Two equivalent representations are presented. The first uses a pair of differential operators which leads to a higher order linear system for ...

Journal: Applicable Analysis, vol. ahead-of-p, no. ahead-of-p, pp. 1-22, 2011]]>A method for symbolically computing conservation laws of nonlinear partial differential equations (PDEs) in multiple space dimensions is presented in the language of variational calculus and linear algebra. The steps of the method are illustrated using the Zakharov–Kuznetsov and Kadomtsev–Petviashvili equations as examples.The method is algorithmic and has been implemented in Mathematica. The software package, ConservationLawsMD.m, ...

Journal: Journal of Symbolic Computation - JSC, vol. 46, no. 12, pp. 1355-1377, 2011]]>The purpose of present research is to derive analytical expressions for the solution of steady MHD convective and slip flow due to a rotating disk. Viscous dissipation and Ohmic heating are taken into account. The nonlinear partial differential equations for MHD laminar flow of the homogeneous fluid are reduced to a system of five coupled ordinary differential equations by using ...

Journal: Communications in Nonlinear Science and Numerical Simulation - COMMUN NONLINEAR SCI NUMER SI, vol. 16, no. 11, pp. 4303-4317, 2011]]>Analysis is carried out to study the convection heat transfer in an upper convected Maxwell fluid at a non-isothermal stretching surface. This is a generalization of the paper by Sadeghy et al. [21] to study the effects of free convection currents, variable thermal conductivity and the variable temperature at the stretching surface. Unlike in Sadeghy et al., here the ...

Journal: Central European Journal of Physics - CENT EUR J PHYS, vol. 9, no. 3, pp. 807-815, 2011]]>Motivated by examples in developmental biology and ecology, we develop a model for convection-dominated invasion of a spatial region by initially motile agents which are able to settle permanently. The motion of the motile agents and their rate of settling are affected by the local concentration of settled agents. The model can be formulated as a nonlinear partial differential ...

Journal: Mathematical Biosciences - MATH BIOSCI, vol. 232, no. 1, pp. 42-56, 2011]]>Following the Weiss-Tabor-Carnevale approach [J. Weiss, M. Tabor, and G. Carnevale, J. Math. Phys. 24, 522 (1983); J. Weiss, M. Tabor, and G. Carnevale, J. Math. Phys. 25, 13 (1984).] designed for studying the integrability properties of nonlinear partial differential equations, we investigate the singularity structure of a (2+1)-dimensional wave-equation describing the propagation of polariton solitary ...

Published in 2011]]>Purpose – The purpose of this paper is to use He's Exp-function method (EFM) to construct solitary and soliton solutions of the nonlinear evolution equation. Design/methodology/approach – This technique is straightforward and simple to use and is a powerful method to overcome some difficulties in the nonlinear problems. Findings – This method is developed for searching exact traveling wave ...

Journal: International Journal of Numerical Methods for Heat & Fluid Flow - INT J NUMER METHOD HEAT FL F, vol. 21, no. 6, pp. 736-753, 2011]]>A one-dimensional model of fox-rabies of two nonlinear partial differential equations of hyperbolic type is studied. Finite difference techniques are applied to compute the numerical solutions of the initial/boundary value problem. The convergence of the resulting schemes, which have a second order accuracy in space and time, is investigated. The method is tested for different values of ...

Journal: International Journal of Computer Mathematics - IJCM, vol. ahead-of-p, no. ahead-of-p, pp. 1-12, 2011]]>We consider the probabilistic numerical scheme for fully nonlinear partial differential equations suggested in [Comm. Pure Appl. Math. 60 (2007) 1081–1110] and show that it can be introduced naturally as a combination of Monte Carlo and finite difference schemes without appealing to the theory of backward stochastic differential equations. Our first main result provides the convergence of the discrete-...

Journal: Annals of Applied Probability - ANN APPL PROBAB, vol. 21, no. 2011, pp. 1322-1364, 2011]]>The determining equations for the nonclassical symmetry reductions of nonlinear partial differential equations with arbitrary order can be obtained by requiring the compatibility between the original equations and the invariant surface conditions. The (2+1)-dimensional shallow water wave equation, Boussinesq equation, and the dispersive wave equations in shallow water serve as examples illustrating how compatibility leads quickly and easily to ...

Published in 2011]]>Recently, many important nonlinear partial differential equations arising in the applied physical and mathematical sciences have been tackled by a popular approach, the so-called Exp-function method. In this paper, we present some shortcomings of this method by analyzing the results of recently published papers. We also discuss the possible improvement of the effectiveness of the method.

Journal: Communications in Theoretical Physics - COMMUN THEOR PHYS, vol. 56, no. 3, pp. 397-403, 2011]]>The Exp-function method with the aid of symbolic computational system can be used to obtain the generalized solitary solutions and periodic solutions for nonlinear evolution equations arising in mathematical physics. In this paper, we study the analytic treatment of the Zakharov-Kuznetsov (ZK) equation, the modified ZK equation, and the generalized forms of these equations. Exact solutions with solitons ...

Journal: International Journal of Modern Physics B - IJMPB, vol. 25, pp. 2965-2981, 2011]]>This paper investigates the transverse vibration of a simply supported nanobeam with an initial axial tension based on the nonlocal stress field theory with a nonlocal size parameter. Considering an axial elongation due to transverse vibration, the internal axial tension is not precisely equal to the external initial tension. A sixth-order nonlinear partial differential equation that governs the transverse ...

Journal: Science China-technological Sciences - SCI CHINA-TECHNOL SCI, vol. 54, no. 8, pp. 2007-2013, 2011]]>In this paper, the generalized differential transform method is implemented for solving several linear fractional partial differential equations arising in fluid mechanics. This method is based on the two-dimensional differential transform method (DTM) and generalized Taylor's formula. Numerical illustrations of the time-fractional diffusion equation and the time-fractional wave equation are investigated to demonstrate the effectiveness of ...

Conference: International Conference on Multimedia Technology - ICMT, 2011]]>Image restoration has been a research topic deeply investigated within the last two decades. As is well-known, total variation (TV) minimization by Rudin, Osher, and Fatami [6] offers superior image restoration quality and involves solving a second order nonlinear partial differential equation (PDE). In more recent years, some effort has been made in improving computational speed for solving the ...

Conference: IEEE International Symposium on Intelligent Signal Processing and Communication Systems - ISPACS, 2011]]>Motivated by ongoing work in the theory of stochastic partial differential equations we develop direct methods to infer that the Galerkin approximations of certain nonlinear partial differential equations are Cauchy (and therefore convergent). We develop such a result for the Navier–Stokes equations in space dimensions two and three, and for the primitive equations in space dimension two. The analysis ...

Journal: Applicable Analysis, vol. 90, no. 1, pp. 85-102, 2011]]>A method of integrable discretization of the Liouville type nonlinear partial differential equations based on integrals is suggested. New examples of the discrete Liouville type models are presented.

Published in 2011]]>A slab of chemically passive microporous ceramic material is attached to the gas sensitive surface of a chemoresistor. When exposed to analyte contaminated air, analyte molecules diffuse through the slab before affecting the sensor. We compared the transient responses of the barrier-equipped sensor with those of a bare device and resulted in the information regarding the rate process of ...

Journal: Measurement Science & Technology - MEAS SCI TECHNOL, vol. 22, no. 8, 2011]]>Implicit particle filtering is a sequential Monte Carlo method for data assim- ilation, designed to keep the number of particles manageable by focussing attention on regions of large probability. These regions are found by min- imizing, for each particle, a scalar function F of the state variables. Some previous implementations of the implicit filter rely on finding the Hessians of ...

Published in 2011]]>A method starting from an equivalent Lie group of transformations instead of Sophus Lie's traditional procedure and using some direct subtle algebraic substitution techniques is devoted, which has been implemented in Maple and serves to seek Lie point symmetry, Lie symmetry groups, the symmetry reductions and the similarity solutions not only for partial differential equation but also for system ...

Conference: Pacific-Asia Conference on Circuits, Communications and Systems - PACCS, 2011]]>The approximate inertial manifolds (AIMs) of Burgers equation is approached by nonlinear Galerkin methods, and it can be used to capture and study the shock wave numerically in a reduced system with low dimension. Following inertial manifolds, the asymptotic behavior of Burgers equation, an infinite dimensional dissipative dynamic systems, will evolve to a compact set known as a global attractor, ...

Journal: Communications in Nonlinear Science and Numerical Simulation - COMMUN NONLINEAR SCI NUMER SI, vol. 16, no. 12, pp. 4666-4670, 2011]]>We study the underlying nonlinear partial differential equation that governs the behaviour of spherically symmetric charged fluids in general relativity. We investigate the conditions for the equation to admit a first integral or be reduced to quadratures using symmetry methods for differential equations. A general Noether first integral is found. We also undertake a comprehensive group analysis of the underlying ...

Journal: Classical and Quantum Gravity - CLASS QUANTUM GRAVITY, vol. 28, no. 10, 2011]]>The determining equations for the nonclassical symmetry reductions of nonlinear partial differential equations with arbitrary order can be obtained by requiring the compatibility between the original equations and the invariant surface conditions. The (2+1)-dimensional shallow water wave equation, Boussinesq equation, and the dispersive wave equations in shallow water serve as examples illustrating how compatibility leads quickly and easily to ...

Journal: Communications in Theoretical Physics - COMMUN THEOR PHYS, vol. 56, no. 4, pp. 611-616, 2011]]>In this survey, results on the existence, growth, uniqueness, and value distribution of meromorphic (or entire) solutions of linear partial differential equations of the second order with polynomial coefficients that are similar or different from that of meromorphic solutions of linear ordinary differential equations have been obtained. We have characterized those entire solutions of a special partial differential equation that ...

Journal: Journal of Mathematical Sciences, vol. 173, no. 2, pp. 201-206, 2011]]>Nonlinear partial differential equation with random Neumann boundary conditions are considered. A stochastic Taylor expansion method is derived to simulate these stochastic systems numerically. As examples, a nonlinear parabolic equation (the real Ginzburg–Landau equation) and a nonlinear hyperbolic equation (the sine–Gordon equation) with random Neumann boundary conditions are solved numerically using a stochastic Taylor expansion method. The impact ...

Journal: Applied Mathematics and Computation - AMC, vol. 217, no. 23, pp. 9532-9542, 2011]]>The dynamic response of a micro-resonator driven by electrostatic combs is investigated in this work. The micro-resonator is assumed to consist of eight flexible beams and three rigid bodies. The nonlinear partial differential equations that govern the motions of the flexible beams are obtained, as well as their boundary and matching conditions. The natural matching conditions for the ...

Journal: Communications in Nonlinear Science and Numerical Simulation - COMMUN NONLINEAR SCI NUMER SI, vol. 16, no. 8, pp. 3425-3442, 2011]]>The dynamic response of a micro-resonator driven by electrostatic combs is investigated in this work. The micro-resonator is assumed to consist of eight flexible beams and three rigid bodies. The nonlinear partial differential equations that govern the motions of the flexible beams are obtained, as well as their boundary and matching conditions. The natural matching conditions for the ...

Journal: Communications in Nonlinear Science and Numerical Simulation - COMMUN NONLINEAR SCI NUMER SI, vol. 16, pp. 3425-3442, 2011]]>Two novel solution schemes for integration and dynamic inversion of a class of population balance equations with size-dependent growth rate are contributed in this article. The proposed methods are developed for population balance systems that, in addition to an advective and a birth rate term, include an external variable which may be fixed (referring to the integration problem), or ...

Journal: Chemical Engineering Science - CHEM ENG SCI, vol. 66, no. 17, pp. 3711-3720, 2011]]>We consider the initial-boundary value problem on a half-line for the KdV equation with Landau damping. We study traditionally important problems of the theory of nonlinear partial differential equations, such as global in time existence of solutions to the initial-boundary value problem and the asymptotic behavior of solutions for large time.

Journal: Fuel and Energy Abstracts, vol. 74, no. 14, pp. 4682-4697, 2011]]>Based on the von Karman plate theory of large deflection, we derive the nonlinear partial differential equation for a rectangular magnetoelectroelastic thin plate under the action of a transverse static mechanical load. By employing the Bubnov–Galerkin method, the nonlinear partial differential equation is transformed to a third-order nonlinear algebraic equation for the maximum deflection where a coupling factor ...

Journal: Mechanics Research Communications - MECH RES COMMUN, vol. 38, no. 7, pp. 518-523, 2011]]>We study multiple solutions of an even-order nonlinear partial differential equation with a Dirichlet boundary condition. A related class of nonlinear systems is investigated.

Journal: Fuel and Energy Abstracts, vol. 74, no. 4, pp. 1345-1354, 2011]]>This paper presents an analytical study on the forced vibration of micro-switches under combined electrostaticc, intermolecular forces and axial residual stress. The micro-switch considered in this study is made of non-homogeneous functionally graded material with two material phases. The nonlinear partial differential equation which describes the forced vvibration of the micro-beam is derived based on the ...

Journal: Procedia Engineering, vol. 14, pp. 280-287, 2011]]>In this paper, non-travelling wave solutions with three arbitrary functions, including the soliton-like solutions periodic form solutions and rational solutions, are obtained by using a improved extended tanh-function method to solve a compound KdV-Burgers equation with the help of Maple. This method can be applied to other higher-dimensional nonlinear partial differential equations.

Conference: International Conference on Computer and Management - CAMAN, 2011]]>We study the nonlinear dynamics of DNA, for longitudinal and transverse motions, in the framework of the microscopic model of Peyrard and Bishop. The coupled nonlinear partial differential equations for dynamics of DNA model, which consists of two long elastic homogeneous strands connected with each other by an elastic membrane, have been solved for solitary wave solution which is further ...

Journal: Physics Letters A - PHYS LETT A, vol. 375, no. 3, pp. 480-483, 2011]]>An electrochemical tubular reactor system, which is used to remove the hexavalent chromium Cr(VI) from wastewaters, is presented. Under specific modeling and operating constraints, the axial dispersion reactor is described by the coupled nonlinear partial differential equations (PDEs) under Danckwerts boundary conditions. Through the composite finite difference combination, the lumped differential-algebraic equations (DAEs) turn out to be a ...

Journal: Journal of The Taiwan Institute of Chemical Engineers - J TAIWAN INST CHEM ENG, vol. 42, no. 3, pp. 498-505, 2011]]>Finding an appropriate turbulence model for a given flow case usually calls for extensive experimentation with both models and numerical solution methods. This work presents the design and implementation of a flexible, programmable software framework for assisting with numerical experiments in computational turbulence. The framework targets Reynolds-averaged Navier-Stokes models, discretized by finite element methods. The novel implementation makes ...

Journal: Advances in Water Resources - ADV WATER RESOUR, vol. abs/1102.2, 2011]]>A Series-connected discrete Josephson transmission line (DJTL) which is periodically loaded by open stubs is studied to investigate various aspects of traveling-wave parametric amplification. The dispersion analysis is made to ensure the existence of three non-degenerate time-harmonic waves interacting with each other through the phase matching condition which is imposed by the cubic nonlinearity associated with ...

Published in 2011]]>Finding an appropriate turbulence model for a given flow case usually calls for extensive experimentation with both models and numerical solution methods. This work presents the design and implementation of a flexible, programmable software framework for assisting with numerical experiments in computational turbulence. The framework targets Reynolds-averaged Navier-Stokes models, discretized by finite element methods. The novel implementation makes ...

Journal: Advances in Water Resources - ADV WATER RESOUR, vol. 34, pp. 1082-1101, 2011]]>Steady mixed convection boundary layer flow from an isothermal horizontal circular cylinder embedded in a porous medium filled with a nanofluid has been studied for both cases of a heated and cooled cylinder. The resulting system of nonlinear partial differential equations is solved numerically using an implicit finite-difference scheme. The solutions for the flow and heat transfer characteristics are ...

Journal: Transport in Porous Media - TRANS POROUS MEDIA, vol. 86, no. 2, pp. 517-536, 2011]]>In catalyst development, a targeted reaction often is inhibited by a strongly adsorbed species. To help develop mitigation means, it is important to quantitatively relate the inhibition dynamics to catalyst properties. The present study develops a combined modeling and experimental approach to address this problem. A general mathematical model consisting of three nonlinear partial differential equations is reduced to quadratures ...

Journal: Chemical Engineering Science - CHEM ENG SCI, vol. 66, no. 6, pp. 1060-1068, 2011]]>The particular challenges of modeling control systems for the middle route of the south-to-north water transfer project are illustrated. Open channel dynamics are approximated by well-known Saint-Venant nonlinear partial differential equations. For better control purpose, the finite difference method is used to discretize the Saint-Venant equations to form the state space model of channel system. ...

Journal: Science China-technological Sciences - SCI CHINA-TECHNOL SCI, vol. 54, no. 4, pp. 781-792, 2011]]>By means of computerized symbolic computation and a modified extended tanh-function method the multiple travelling wave solutions of nonlinear partial differential equations is presented and implemented in a computer algebraic system. Applying this method, we consider some of nonlinear partial differential equations of special interest in nanobiosciences and biophysics namely, the transmission line models of microtubules for nano-ionic ...

Journal: Applied Mathematics and Computation - AMC, vol. 218, no. 7, pp. 3499-3506, 2011]]>We study the general model of self-financing trading strategies in illiquid markets introduced by Schönbucher and Wilmott (SIAM J Appl Math 61(1):232–272, 2000). A hedging strategy in the framework of this model satisfies a nonlinear partial differential equation (PDE) which contains some function g(α). This function is deeply connected to a marginal utility function. We ...

Journal: Letters in Mathematical Physics - LETT MATH PHYS, vol. 96, no. 1, pp. 191-207, 2011]]>Following the Weiss-Tabor-Carnevale approach [J. Weiss, M. Tabor, and G. Carnevale, J. Math. Phys. 24, 522 (1983); J. Weiss, M. Tabor, and G. Carnevale, J. Math. Phys. 25, 13 (1984).] designed for studying the integrability properties of nonlinear partial differential equations, we investigate the singularity structure of a (2+1)-dimensional wave-equation describing the propagation of polariton solitary ...

Published in 2011]]>We consider the initial–boundary value problem for the Ott–Sudan–Ostrovskiy equation on a half-line. We study traditionally important problems of the theory of nonlinear partial differential equations, such as global in time existence of solutions to the initial–boundary value problem and the asymptotic behavior of solutions for large time.

Journal: Journal of Differential Equations - J DIFFERENTIAL EQUATIONS, vol. 250, no. 12, pp. 4262-4288, 2011]]>This paper deals with the numerical analysis and computing of a nonlinear model of option pricing appearing in illiquid markets with observable parameters for derivatives. A consistent monotone finite difference scheme is proposed and a stability condition on the stepsize discretizations is given.

Journal: Computers & Mathematics With Applications - COMPUT MATH APPL, vol. 61, no. 8, pp. 1951-1956, 2011]]>The vibration of an Euler–Bernoulli beam, resting on a nonlinear Kelvin–Voight viscoelastic foundation, traversed by a moving load is studied in the frequency domain. The objective is to obtain the frequency responses of the beam and the effects of different parameters on the system response. The parameters include the magnitude and speed of the moving load and the ...

Journal: Journal of Sound and Vibration - J SOUND VIB, vol. 330, no. 7, pp. 1455-1471, 2011]]>