APPROXIMATION OF STOCHASTIC ADVECTION DIFFUSION EQUATIONS WITH STOCHASTIC CRANK{NICOLSON SCHEME

In this paper, an unconditionally stable stochastic diferencescheme is proposed for the numerical solution of It^o stochastic advectiondiffusion equation with one dimensional white noise process. The mainproperties of deterministic difference schemes, i.e., consistency, stabilityand convergency are developed for the stochastic case. It is shown throughanalysis that the proposed scheme has these properties. Numerical resultsare given to demonstrate the computational e ciency of the stochasticscheme.

Keywords:

Stochastic partial diferential equations , Stochastic nite diference scheme , Stability , Consistency , Convergency