Analytical and numerical stability of neutral delay integro-differential equations and neutral delay partial differential equations

This paper is concerned with the analytical and numerical stability of neutral delay integro-differential equations (NDIDEs) and neutral delay partial differential equations (NDPDEs). We study the delay-dependent stability of the real coefficient linear test equations for NDIDEs. Furthermore, we prove that the trapezium rule can preserve the delay-dependent stability of the test equations considered. We also discuss the delay-dependent stability of the continuous problems, the semi-discrete problems and the fully discrete problems of linear NDPDEs. Some numerical experiments are given to confirm the theoretical results.