A numerical method for the semilinear stochastic transport equation

Hugo de la Cruz, Christian H. Olivera, Jorge P. Zubelli


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.


Stochastic partial differential equations, numerical methods, stochastic transport equation, local linearization approach, exponential integrators

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DOI: https://doi.org/10.5540/03.2015.003.01.0309


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