Numerics of stochastic parabolic differential equations with stable finite difference schemes

Document Type: Regular Paper


1 Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran

2 Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran


In the present article, we focus on the numerical approximation of stochastic partial differential equations of Itˆo type with space-time white noise process, in particular, parabolic equations. For each case of additive and
multiplicative noise, the numerical solution of stochastic diffusion equations is approximated using two stochastic finite difference schemes and the stability and consistency conditions of the considered methods are analyzed. Numerical results are given to demonstrate the computational efficiency of the stochastic methods.