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

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arxiv 1812.09036 v2 pith:WQB7ZYH4 submitted 2018-12-21 math.NA cs.NA

Stuart Campbell , Gabriel Lord This is my paper · ORCID
classification math.NAcs.NA
keywords time-steppingadaptiveconvergencediscretisationdriftstrongaccurateadapting
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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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Cited by 1 Pith paper

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  1. Strong convergence of an adaptive time-stepping Milstein method for SDEs with monotone coefficients

    math.NA 2019-08 conditional novelty 6.0 of 10

    An explicit adaptive Milstein method with path-bounded time stepping is shown to converge strongly with order one for SDEs with one-sided Lipschitz drift and non-commutative noise.

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