Approximation of stochastic advection-diffusion equation using compact finite difference technique

Document Type: Regular Paper


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

2 The Center of Excellence on Modeling and Control Systems, Department of applied Mathematics, School of Mathematical science, Ferdowsi University of Mashhad, Mashhad


In this paper, we propose a new method for solving the stochastic advection-diffusion equation of Ito type. In this work, we use a compact finite difference approximation for discretizing spatial derivatives of the mentioned equation and semi-implicit Milstein scheme for the resulting linear stochastic system of differential equation. The main purpose of this paper is the stability investigation of the applied method. Finally, some numerical examples are provided to show the accuracy and efficiency of the proposed technique.