Convergence and stability of the semi-implicit Euler method for linear stochastic delay integro-differential equations

Abstract

This paper deals with the convergence and stability of the semi-implicit Euler method for linear stochastic delay integro-differential equations. It is proved that the semi-implicit Euler method is convergent with strong order p=0.5. The condition under which the method is asymptotic mean square stable is determined and numerical experiments are presented.

Keywords:

• Stochastic delay integro-differential equations
• Mean square stability
• Semi-implicit Euler method
• Numerical solution