McDonald, Stuart
(2006):
*Finite Difference Approximation for Linear Stochastic Partial Differential Equations with Method of Lines.*

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## 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.

Item Type: | MPRA Paper |
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Institution: | Social and Information Systems Laboratory, California Institute of Technology |

Original Title: | Finite Difference Approximation for Linear Stochastic Partial Differential Equations with Method of Lines |

Language: | English |

Keywords: | Finite difference approximation; linear stochastic partial differential equations (SPDEs); the method of lines (MOL) |

Subjects: | C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63 - Computational Techniques ; Simulation Modeling |

Item ID: | 3983 |

Depositing User: | Stuart McDonald |

Date Deposited: | 11 Jul 2007 |

Last Modified: | 28 Sep 2019 12:07 |

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URI: | https://mpra.ub.uni-muenchen.de/id/eprint/3983 |