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Numerical Solution of Wick-Stochastic Partial Differential Equations

In: Proceedings of the International Conference on Stochastic Analysis and Applications

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  • Thomas Gorm Theting

    (Norwegian University of Science and Technology, Department of Mathematical Sciences)

Abstract

We consider the numerical approximation of linear Wick-stochastic boundary value problems of elliptic and parabolic type. Numerical methods based on a Galerkin type of approximation are described and convergence results are reported. To illustrate the approach we consider three specific examples: The stochastic Poisson equation, the parabolic Wick-stochastic pressure equation, and a Wick version of the viscous Burgers’ equation with stochastic source. The latter example is nonlinear and falls outside the scope of the theory, but the ideas still can be applied and numerical results are reported.

Suggested Citation

  • Thomas Gorm Theting, 2004. "Numerical Solution of Wick-Stochastic Partial Differential Equations," Springer Books, in: Sergio Albeverio & Anne Boutet de Monvel & Habib Ouerdiane (ed.), Proceedings of the International Conference on Stochastic Analysis and Applications, pages 303-349, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4020-2468-9_18
    DOI: 10.1007/978-1-4020-2468-9_18
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