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Pré-Publication, Document De Travail Année : 2023

Analysis of a positivity-preserving splitting scheme for some nonlinear stochastic heat equations

Résumé

We construct a positivity-preserving Lie-Trotter splitting scheme with finite difference discretization in space for approximating the solutions to a class of nonlinear stochastic heat equations with multiplicative space-time white noise. We prove that this explicit numerical scheme converges in the mean-square sense, with rate 1/4 in time and rate 1/2 in space, under appropriate CFL conditions. Numerical experiments illustrate the superiority of the proposed numerical scheme compared with standard numerical methods which do not preserve positivity.
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hal-04077860 , version 1 (21-04-2023)

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  • HAL Id : hal-04077860 , version 1

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Charles-Edouard Bréhier, David Cohen, Johan Ulander. Analysis of a positivity-preserving splitting scheme for some nonlinear stochastic heat equations. 2023. ⟨hal-04077860⟩
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