Finite difference approximation for stochastic parabolic partial differential equations

Abstract

Differential equations, especially partial differential equations (PDES) have wide range of applications in sciences, finance (economics), Engineering and so forth. In last decade, substantial amount of work has been done in studying stochastic partial differential equations (SPDES). A SPDE is a PDE containing a random ‘noise’ term. SPDES have no analytical solutions. Various numerical methods have been developed from time to time and tested for their validity using Matlab program. In this thesis, the author will discuss the finite difference method for stochastic parabolic partial differential equations. Matlab software is used for simulation of the solution of this equation. The main objective of this thesis is to investigate the finite difference approximation of a stochastic parabolic partial differential equation with white noise. The author discusses alternative proof for error bounds using Green function in support of this method.