High order compact finite difference scheme for stochastic advection – diffusion equations (SCDEs) of Ito type is designed. Firstly, Modified Mathematical formulation of the stochastic advection – diffusion was developed, followed by the derivation of stochastic differential advection – diffusion using compact finite difference schemes. Explicit- implicit Euler’s scheme was adopted to established the stability criteria in the resulting linear stochastic system of differential equations. The stability criterion was investigated using Fourier mode. Numerical examples were conducted to test the validity, efficient, accuracy and robustness of the derived schemes.
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