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Mathematics > Numerical Analysis

arXiv:1812.09036 (math)
[Submitted on 21 Dec 2018 (v1), last revised 21 Aug 2019 (this version, v2)]

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

Authors: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.
Comments: 32 pages, 4 figures
Subjects: Numerical Analysis (math.NA)
MSC classes: (Primary) 65C30, 60H15, 65N12
Cite as: arXiv:1812.09036 [math.NA]
  (or arXiv:1812.09036v2 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.1812.09036

Submission history

From: Stuart Campbell Mr [view email]
[v1] Fri, 21 Dec 2018 10:26:25 UTC (461 KB)
[v2] Wed, 21 Aug 2019 14:16:57 UTC (460 KB)
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