A numerical method for the semilinear stochastic transport equation

Abstract

We propose a new numerical method for the computer simulation of the semi-linear stochastic transport equation. Based on the stochastic characteristic method and the Local Linearization technique, we construct an efficient and stable method for integrating this equation. For this purpose, a suitable exponential-based approximation to the solution of an associated auxiliary random integral equation, together with a Padé method with scaling and squaring strategy are conveniently combined. Results on the convergence and stability of the suggested method and details on its efficient implementation are discussed.