Abstract The aim of this paper is the analysis exponential mean-square stability properties nonlinear stochastic linear multistep methods. In particular it known that, under certain hypothesis on drift and diffusion terms equation, contractivity visible: qualitative feature exact problem here analysed numerical perspective, to understand whether a method can provide an analogous behaviour which...

This paper examines stability analysis of two classes of improved backward Euler methods, namely split-step $(theta, lambda)$-backward Euler (SSBE) and semi-implicit $(theta,lambda)$-Euler (SIE) methods, for nonlinear neutral stochastic delay differential equations (NSDDEs). It is proved that the SSBE method with $theta, lambdain(0,1]$ can recover the exponential mean-square stability with some...