Numerical Stability of Delay Integro-Differential Equations under Resolvent Conditions

摘要

This paper deals with the stability of numerical methods for the delay integro-differential equations. The theta-methods are applied to this system by using the linear interpolation. The upper bound of norm for the corresponding iterative matrix is studied under a weak version for the resolvent conditions of Kreiss. It is proved that the system would preserve its stable properties if theta in [1/2, 1].