In this paper, we present a class of explicit numerical methods for stiff Itô stochastic differential equations (SDEs). These methods are as simple to program and to use as the well-known Euler-Maruyama method, but much more efficient for stiff SDEs. For such problems, it is well known that standard explicit methods face step-size reduction. While semi-implicit methods can avoid these problems ...

In this paper we introduce a new class of explicit one-step methods of order 2 that can be used for solving stiff problems. This class constitutes a generalization of the two-stage explicit Runge-Kutta methods, with the property of having an A-stability region that varies during the integration in accordance with the accuracy requirements. Some numerical experiments on classical stiff problems ...

A detailed account of the stability and accuracy properties of the SBP-SAT technique for numerical time integration is presented. We show how the technique can be used to formulate both global and multi-stage methods with high order of accuracy for both stiff and non-stiff problems. Linear and nonlinear stability results, including A-stability, L-stability and B-stability are proven using the e...