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arXiv · 1812.09036

Adaptive time-stepping for Stochastic Partial Differential Equations with non-Lipschitz drift

Stuart Campbell·Gabriel Lord
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Abstract

We introduce an explicit, adaptive time-stepping scheme for the simulation of SPDEs with one-sided Lipschitz drift coefficients. Strong convergence rates are proven for the full space-time discretisation with multiplicative trace-class noise by considering the space and time discretisation separately. Adapting the time-step size to ensure strong convergence is shown numerically to produce more accurate solutions when compared to alternative fixed time-stepping strategies for the same computational effort.

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Stuart Campbell, Gabriel Lord. 2018-12-21. Adaptive time-stepping for Stochastic Partial Differential Equations with non-Lipschitz drift. https://arxiv.org/abs/1812.09036

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