A Numerical method for the semilinear stochastic transport equation

Abstract

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