Semi-implicit split-step numerical methods for a class of nonlinear stochastic differential equations with non-Lipschitz drift terms

摘要

In this paper, we discuss numerical solutions of a class of nonlinear stochastic differential equations using semi-implicit split-step methods. Under some monotonicity conditions on the drift term, we study moment estimates and strong convergence properties of the numerical solutions, with a focus on stochastic Ginzburg-Landau equations. Moreover, we compare the performance of various numerical methods, including the tamed Euler, truncated Euler, implicit Euler and split-step procedures. In particular, we discuss the empirical rate of convergence and the computational cost of these methods for certain parameter values of the models used. (C) 2018 Elsevier B.V. All rights reserved.