S-ROCK methods for stochastic delay differential equations with one fixed delay

Abstract

We propose stabilized explicit stochastic Runge–Kutta methods of strong order one half for Itô stochastic delay differential equations with one fixed delay. The family of the methods is constructed by embedding Runge–Kutta–Chebyshev methods of order one for ordinary differential equations. The values of a damping parameter of the methods are determined appropriately in order to obtain excellent mean square stability properties. Numerical experiments are carried out to confirm their order of convergence and stability properties.