Adaptive time-stepping for Stochastic Partial Differential Equations with non-Lipschitz drift
Numerical Analysis
2019-08-27 v2 Numerical Analysis
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.
Cite
@article{arxiv.1812.09036,
title = {Adaptive time-stepping for Stochastic Partial Differential Equations with non-Lipschitz drift},
author = {Stuart Campbell and Gabriel Lord},
journal= {arXiv preprint arXiv:1812.09036},
year = {2019}
}
Comments
32 pages, 4 figures