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 spacetime 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 

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:  13. Feb 2013 07:57 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/3983 