We have introduced a new explicit numerical method, based on a discrete stochastic process, for solving a class of fractional partial differential equations that model reaction subdiffusion. The scheme is derived from the master equations for the evolution of the probability density of a sum of discrete time random walks. We show that the diffusion limit of the master equations recovers the fra...

In this paper, we study the stability of quasilinear parabolic stochastic partial differential equations with multiplicative noise, which are neither monotone nor locally monotone. The exponential mean square and pathwise solutions established. Moreover, under certain hypothesis on perturbations, can be derived, without utilizing stability.

This paper develops a fractional stochastic partial differential equation (SPDE) to model the evolution of random tangent vector field on unit sphere. The SPDE is governed by diffusion operator Lévy-type behaviour spatial solution, derivative in time depict intermittency its temporal and driven vector-valued Brownian motion sphere characterize long-range dependence. solution presented form Kar...

We study the error of the Euler scheme applied to a stochastic partial differential equation. We prove that as it is often the case, the weak order of convergence is twice the strong order. A key ingredient in our proof is Malliavin calculus which enables us to get rid of the irregular terms of the error. We apply our method to the case a semilinear stochastic heat equation driven by a space-ti...

Stochastic models of chemical systems are often analysed by solving the corresponding Fokker-Planck equation which is a drift-diffusion partial differential equation for the probability distribution function. Efficient numerical solution of the Fokker-Planck equation requires adaptive mesh refinements. In this paper, we present a mesh refinement approach which makes use of a stochastic simulati...