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

Authors:
Jingjun Zhao;Yan Fan;Yang Xu
Affiliations:
Department of Mathematics, Harbin Institute of Technology, Harbin, China 150001;Department of Mathematics, Harbin Institute of Technology, Harbin, China 150001;Department of Mathematics, Harbin Institute of Technology, Harbin, China 150001
Venue:
Numerical Algorithms
Year:
2014

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Abstract

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 (ETR$_2$s), 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.