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Finite Difference Approximation for Linear Stochastic Partial Differential Equations with Method of Lines

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  • McDonald, Stuart

Abstract

A stochastic partial differential equation, or SPDE, describes the dynamics of a stochastic process defined on a space-time continuum. This paper provides a new method for solving SPDEs based on the method of lines (MOL). MOL is a technique that has largely been used for numerically solving deterministic partial differential equations (PDEs). MOL works by transforming the PDE into a system of ordinary differential equations (ODEs) by discretizing the spatial dimension of the PDE. The resulting system of ODEs is then solved by application of either a finite difference or a finite element method. This paper provides a proof that the MOL can be used to provide a finite difference approximation of the boundary value solutions for two broad classes of linear SPDEs, the linear elliptic and parabolic SPDEs.

Suggested Citation

  • McDonald, Stuart, 2006. "Finite Difference Approximation for Linear Stochastic Partial Differential Equations with Method of Lines," MPRA Paper 3983, University Library of Munich, Germany, revised 30 May 2007.
    • Handle: RePEc:pra:mprapa:3983
    as

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    References listed on IDEAS

    as
    1. Ma, Jin & Yong, Jiongmin, 1997. "Adapted solution of a degenerate backward spde, with applications," Stochastic Processes and their Applications, Elsevier, vol. 70(1), pages 59-84, October.
    2. Alan Brace & Marek Musiela, 1994. "A Multifactor Gauss Markov Implementation Of Heath, Jarrow, And Morton," Mathematical Finance, Wiley Blackwell, vol. 4(3), pages 259-283, July.
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    More about this item

    Keywords

    Finite difference approximation; linear stochastic partial differential equations (SPDEs); the method of lines (MOL);
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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