Adaptive timestepping for S(P)DEs to control growth.

We introduce a class of adaptive timestepping strategies for stochastic differential equations such as those arising from the semi-discretization of SPDEs with non-Lipschitz drift coefficients. These strategies work by controlling potential unbounded growth in solutions of a numerical scheme. We prove that the Euler-Maruyama scheme with an adaptive timestepping strategy in this class is strongly convergent and present preliminary results on a semi-implicit scheme and an extension to non-Lipschitz noise terms. We test this alternative to taming on some examples. This is joint work with Conall Kelly.