The authors consider a scalar linear system of Itô stochastic delay differential equations
where is on dimensional standard Wiener process, A split-step backward Euler (SSBE) scheme for solving this system is constructed. The authors constructed the SSBE method by when , and when
where is the numerical approximation of with The following theorem is the main result of this paper.
Theorem: Assume the condition is satisfied.
if and then the SSBE method is general mean spare-stable
if and then the SSBE methods is MS-stable and the stepsize satisfies
if then the SSBE methods is MS-stable and the stepsize satisfies where
Several illustrative numerical examples of applying the SSBE method are presented.