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Stability of Runge-Kutta-Pouzet methods for Volterra integro-differential equations with delays

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Abstract

This paper is concerned with the study of the stability of Runge-Kutta-Pouzet methods for Volterra integro-differential equations with delays. We are interested in the comparison between the analytical and numerical stability regions. First, we focus on scalar equations with real coefficients. It is proved that all Gauss-Pouzet methods can retain the asymptotic stability of the analytical solution. Then, we consider the multidimensional case. A new stability condition for the stability of the analytical solution is given. Under this condition, the asymptotic stability of Gauss-Pouzet methods is investigated.

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Authors and Affiliations

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

    Chengming Huang

  2. Department of Computerscience, Katholieke Universiteit Leuven, Celestijnenlaan 200A, B3001, Leuven, Belgium

    Stefan Vandewalle

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  1. Chengming Huang
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  2. Stefan Vandewalle
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Correspondence to Chengming Huang.

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Huang, C., Vandewalle, S. Stability of Runge-Kutta-Pouzet methods for Volterra integro-differential equations with delays. Front. Math. China 4, 63–87 (2009). https://doi.org/10.1007/s11464-009-0008-6

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  • DOI: https://doi.org/10.1007/s11464-009-0008-6

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