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Stability criteria for exact and discrete solutions of neutral multidelay-integro-differential equations

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Abstract

This paper deals with the asymptotic stability of exact and discrete solutions of neutral multidelay-integro-differential equations. Sufficient conditions are derived that guarantee the asymptotic stability of the exact solutions. Adaptations of classical Runge–Kutta and linear multistep methods are suggested for solving such systems with commensurate delays. Stability criteria are constructed for the asymptotic stability of these numerical methods and compared to the stability criteria derived for the continuous problem. It is found that, under suitable conditions, these two classes of numerical methods retain the stability of the continuous systems. Some numerical examples are given that illustrate the theoretical results.

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Authors and Affiliations

  1. Department of Mathematics, Huazhong University of Science and Technology, Wuhan, 430074, China

    Chengjian Zhang

  2. Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, B-3001, Leuven, Belgium

    Stefan Vandewalle

Authors
  1. Chengjian Zhang
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  2. Stefan Vandewalle
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Correspondence to Chengjian Zhang.

Additional information

Communicated by A. Iserless.

This research is supported by Fellowship F/02/019 of the Research Council of the K.U.Leuven, NSFC (No.10571066) and SRF for ROCS, SEM.

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Zhang, C., Vandewalle, S. Stability criteria for exact and discrete solutions of neutral multidelay-integro-differential equations. Adv Comput Math 28, 383–399 (2008). https://doi.org/10.1007/s10444-007-9037-4

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  • DOI: https://doi.org/10.1007/s10444-007-9037-4

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