Seminar in Numerical Analysis: Gabriel Lord (Radboud University Nijmegen)

Adaptive time-stepping for S(P)DEs with non-Lipschitz drift

We examine how time step adaptivity can be used to control potential instability arising from non-Lipschitz terms for stochastic partial differential equations (SPDEs). I will give a brief introduction to SPDEs and illustrate the stability issue with the standard uniform step Euler method to motivate the adaptive method. I will present a strong convergence result and outline the steps of the proof. To illustrate the method we examine the stochastic Allen-Cahn, Swift-Hohenberg,  Kuramoto-Sivashinsky equations and finally will discuss a potential use of the adaptivity for the deterministic system. This is joint work with Stuart Campbell.

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