A stepsize control algorithm for SDEs with small noise based on stochastic Runge-Kutta Maruyama methods
A variable stepsize control algorithm for the solution of ordinary stochastic differential equations (SDEs) with a small noise parameter \(\epsilon\) is presented and applied to some examples. For the optimal stepsize for each stage of the algorithm, an estimate of the global error is exploited, based on the local error of stochastic Runge-Kutta Maruyama (SRKM) methods. Variable step size algorithms based on stochastic Runge-Kutta methods were also presented by \textit{T. A. Averina} et al. [Bull. Novosib. Comput. Cent., Ser. Numer. Anal. 1995, No. 6, 9--27 (1995; Zbl 0906.65143)].
scientific article; zbMATH DE number 6110507
scientific article