Mean Square Convergent Finite Difference Scheme for Stochastic Parabolic PDEs

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.

A numerical scheme for solutions of stochastic advection-diffusion equations

“…Apparently, appropriate algorithms that can approximate these equations have attracted many researchers since we can hardly find explicit formula of the corresponding solutions. In [2], [3], [4], [5], the authors studied the weak and the strong numerical schemes for SPDEs.…”

Numerical Solution of Stochastic Generalized Fractional Diffusion Equation by Finite Difference Method

“…More recently, the development of numerical methods for the approximation of SDEs has become a field of increasing interest, since analytical solutions of SDEs are not usually available [2]. In recent years, some of the main numerical methods for solving stochastic partial differential equations (SPDEs), like finite difference and finite element schemes, have been considered [3][4][5] (e.g., [6][7][8]), based on a finite difference scheme in both space and time.…”

The Studying of Random Cauchy Convection Diffusion Models under Mean Square and Mean Fourth Calculus

“…Natural phenomena laws are usually enough to derive this equation. Random models can be also used to derive this equation, with the worthy advantage that they provide us with informations about the statistical properties for activity of particle [9,10].…”