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Adaptive time-stepping for Stochastic Partial Differential Equations with non-Lipschitz drift (1812.09036v2)
Published 21 Dec 2018 in math.NA and cs.NA
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.