Stability of Runge-Kutta-Pouzet methods for Volterra integro-differential equations with delays |
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Authors: | Chengming Huang Stefan Vandewalle |
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Institution: | 1. School of Mathematics and Statistics, Huazhong University of Science and Technology,Wuhan 430074, China; 2. Department of Computerscience, Katholieke Universiteit Leuven, Celestijnenlaan 200A,B3001 Leuven, Belgium |
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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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Keywords: | Volterra delay integro-differential equation asymptotic stability Runge-Kutta-Pouzet method |
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