TITLE:
Mean Square Convergent Finite Difference Scheme for Stochastic Parabolic PDEs
AUTHORS:
W. W. Mohammed, M. A. Sohaly, A. H. El-Bassiouny, K. A. Elnagar
KEYWORDS:
Stochastic Partial Differential Equations, Mean Square Sense, Second Order Random Variable, Finite Difference Scheme
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.4 No.4,
August
29,
2014
ABSTRACT: Stochastic partial differential equations (SPDEs) describe the dynamics
of stochastic processes depending on space-time continuum. These equations have
been widely used to model many applications in engineering and mathematical
sciences. In this paper we use three finite difference schemes in order to
approximate the solution of stochastic parabolic partial differential
equations. The conditions of the mean square convergence of the numerical
solution are studied. Some case studies are discussed.