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NUMERICS OF THE VAN-DER-POL EQUATION WITH RANDOM PARAMETER

NUMERICS OF THE VAN-DER-POL EQUATION WITH RANDOM PARAMETER,F. Augustin,P. Rentrop

NUMERICS OF THE VAN-DER-POL EQUATION WITH RANDOM PARAMETER  
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In this article, the problem of long-term integration in the Wiener-Hermite calculus for ordinary differential equations with random parameters is discussed. The Wiener-Hermite calculus is known to lose accuracy with increasing time, even if it provides good results for short times. This is demonstrated for the Van-der-Pol equation with a random parameter. To reduce this problem, the adapted stochastic spectral method (aSSM), which is based on the work of P. Vos (8), is presented. Applying aSSM to the Van-der-Pol equation reduces the error considerably and allows an accurate long-term integration.
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