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arXiv · 2412.08299

An Exponential Stochastic Runge-Kutta Type Method of Order up to 1.5 for SPDEs of Nemytskii-type

Claudine von Hallern·Ricarda Mißfeldt·Andreas Rößler
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Abstract

For the approximation of solutions for stochastic partial differential equations, numerical methods that obtain a high order of convergence and at the same time involve reasonable computational cost are of particular interest. We therefore propose a new numerical method of exponential stochastic Runge-Kutta type that allows for convergence with a temporal order of up to 3/2 and that can be combined with several spatial discretizations. The developed family of derivative-free schemes is tailored to stochastic partial differential equations of Nemytskii-type, i.e., with pointwise multiplicative noise operators. We prove the strong convergence of these schemes in the root mean-square sense and present some numerical examples that reveal the theoretical results.

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Claudine von Hallern, Ricarda Mißfeldt, Andreas Rößler. 2024-12-11. An Exponential Stochastic Runge-Kutta Type Method of Order up to 1.5 for SPDEs of Nemytskii-type. https://arxiv.org/abs/2412.08299

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