Springer Iranian Journal of Science 2731-8095 37 3.1 2013 09 16 Approximation of stochastic advection-diffusion equation using compact finite difference technique 327 333 1631 10.22099/ijsts.2013.1631 EN M. Bishehniasar Department of Mathematics, University of Sistan and Baluchestan Zahedan, Iran A. R. Soheili The Center of Excellence on Modeling and Control Systems, Department of applied Mathematics, School of Mathematical science, Ferdowsi University of Mashhad, Mashhad Journal Article 2012 05 12 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. Stochastic partial differential equation compact finite difference scheme Stability semi-implicit Milstein method https://ijsts.shirazu.ac.ir/article_1631_22e92753f3dad7596b3b82cbc3100358.pdf