Delay‐dependent stability analysis of symmetric boundary value methods for linear delay integro‐differential equations

The paper is concerned with the numerical stability of linear delay integro‐differential equations (DIDEs) with real coefficients. Four families of symmetric boundary value method (BVM) schemes, namely the Extended Trapezoidal Rules of first kind (ETRs) and second kind (ETR2s), the Top Order Methods (TOMs) and the B‐spline linear multistep methods (BS methods) are considered in this paper. We analyze the delay‐dependent stability region of symmetric BVMs by using the boundary locus technique. Furthermore, we prove that under suitable conditions the symmetric schemes preserve the delay‐dependent stability of the test equation. Numerical experiments are given to confirm the theoretical results.