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

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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.

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Authors and Affiliations

  1. Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, China

    Jingjun Zhao, Yan Fan & Yang Xu

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  1. Jingjun Zhao
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  2. Yan Fan
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  3. Yang Xu
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Corresponding author

Correspondence to Yang Xu.

Additional information

This work was supported by the National Natural Science Foundation of China (11101109, 11271102), the Natural Science Foundation of Hei-long-jiang Province of China (A201107) and SRF for ROCS, SEM.

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Zhao, J., Fan, Y. & Xu, Y. Delay-dependent stability analysis of symmetric boundary value methods for linear delay integro-differential equations. Numer Algor 65, 125–151 (2014). https://doi.org/10.1007/s11075-013-9698-7

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  • DOI: https://doi.org/10.1007/s11075-013-9698-7

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