A numerical method for the semilinear stochastic transport equation

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

Resumo


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.

Palavras-chave


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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