Approximation of stochastic advection diffusion eq

Authors: Ali R Soheili Mahdieh Arezoomandan

Publish Date: 2013/07/31

Volume: 58, Issue: 4, Pages: 439-471

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Abstract

The numerical solutions of stochastic partial differential equations of Itô type with time white noise process using stable stochastic explicit finite difference methods are considered in the paper Basically Stochastic Alternating Direction Explicit SADE finite difference schemes for solving stochastic time dependent advectiondiffusion and diffusion equations are represented and the main properties of these stochastic numerical methods eg stability consistency and convergence are analyzed In particular it is proved that when stable alternating direction explicit schemes for solving linear parabolic PDEs are developed to the stochastic case they retain their unconditional stability properties applying to stochastic advectiondiffusion and diffusion SPDEs Numerically unconditional stable SADE techniques are significant for approximating the solutions of the proposed SPDEs because they do not impose any restrictions for refining the computational domains The performance of the proposed methods is tested for stochastic diffusion and advectiondiffusion problems and the accuracy and efficiency of the numerical methods are demonstrated

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