An analysis of delay-dependent stability of symmetric boundary value methods for the linear neutral delay integro-differential equations with four parameters

The paper is concerned with the study of delay-dependent stability of symmetric boundary value methods (BVMs) for the linear neutral delay integro-differential equations (NDIDEs) with four parameters. Four families of symmetric BVMs, namely the Extended Trapezoidal Rules of first (ETRs) and second kind (ETR2s), the Top Order Methods (TOMs) and the B-spline linear multistep methods (BS methods) are considered in this paper. By using the boundary locus technique, the delay-dependent stability region of symmetric BVMs is analyzed and their boundary loci are discussed. In addition, we give a sufficient condition that symmetric BVMs preserve the delay-dependent stability of the analytical solution. Some numerical examples are presented to validate the theoretical results.