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Keywords
(5)
Finite Element
Finite Element Method
Random Process
Stochastic Partial Differential Equation
White Noise
Related Publications
(21)
Numerical solution of stochastic differential equations
Convergence of numerical schemes for the solution of parabolic stochastic partial differential equations
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Finite Element and Difference Approximation of Some Linear Stochastic Partial Differential Equations
Finite Element and Difference Approximation of Some Linear Stochastic Partial Differential Equations,E. j. Allen,S. j. Novosel,Z. Zhang
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Finite Element and Difference Approximation of Some Linear Stochastic Partial Differential Equations
(
Citations: 39
)
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E. j. Allen
,
S. j. Novosel
,
Z. Zhang
Difference and
finite element
methods are described, analyzed, and tested for numericalsolution of linear parabolic and elliptic SPDEs driven by white noise. Weak andintegral formulations of the stochastic partial differential equations are approximated,respectively, by
finite element
and difference methods. The
white noise
processes areapproximated by piecewise constant random processes to facilitate convergence proofsfor the
finite element
method. Error analyses of the two numerical...
Published in 1996.
Cumulative
Annual
Citation Context
(17)
...Before deriving the stochastic partial differential equations, it is useful to consider several properties of Brownian sheets [
4
,
8
,
18
]...
Ummugul Bulut
,
et al.
Derivation of SPDEs for Correlated Random Walk Transport Models in One...
...For parabolic and elliptic SPDEs, finite element and finite difference methods are analysed in
2
...
Jungmin Choi
,
et al.
Approximation and application of the Musiela stochastic PDE in forward...
...Before deriving the stochastic reactiondiffusion equations, it is useful to consider several properties of Brownian sheets [
4
,
10
,
30
]...
Elife Dogan
,
et al.
Derivation of Stochastic Partial Differential Equations for ReactionD...
...The analyses of these models have contributed new insights into the effect of randomness on population dynamics
4
8
9
12
16
...
Azmy S. Ackleh
,
et al.
Stochastic juvenile–adult models with application to a green tree frog...
...It can be shown that the probability density of solutions of the stochastic system (<0001" reftype="dispformula">1) or (<0002" reftype="dispformula">2) approximates the probability density of the original randomly varying process [
1
,
2
,
5
]...
E. J. Allen
.
Stochastic difference equations and a stochastic partial differential ...
References
(1)
Numerical solution of stochastic differential equations
(
Citations: 1795
)
P. E. Kloeden
,
E. Platen
Published in 1992.
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Citations
(39)
Derivation of SPDEs for Correlated Random Walk Transport Models in One and Two Dimensions
Ummugul Bulut
,
Edward J. Allen
Journal:
Stochastic Analysis and Applications  STOCHASTIC ANAL APPL
, vol. 30, no. 4, pp. 553567, 2012
Approximation and application of the Musiela stochastic PDE in forward rate models
Jungmin Choi
,
Max Gunzburger
Journal:
International Journal of Computer Mathematics  IJCM
, vol. aheadofp, no. aheadofp, pp. 112, 2012
Derivation of Stochastic Partial Differential Equations for ReactionDiffusion Processes
Elife Dogan
,
Edward J. Allen
Journal:
Stochastic Analysis and Applications  STOCHASTIC ANAL APPL
, vol. 29, no. 3, pp. 424443, 2011
Stochastic juvenile–adult models with application to a green tree frog population
Azmy S. Ackleh
,
Keng Deng
,
Qihua Huang
Journal:
Journal of Biological Dynamics
, vol. 5, no. 1, pp. 6483, 2011
A Break of the Complexity of the Numerical Approximation of Nonlinear SPDEs with Multiplicative Noise
(
Citations: 2
)
Arnulf Jentzen
,
Michael Roeckner
Published in 2010.