Stability criteria for exact and discrete solutions of neutral multidelay-integro-differential equations |
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Authors: | Chengjian Zhang Stefan Vandewalle |
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Institution: | (1) Department of Mathematics, Huazhong University of Science and Technology, Wuhan, 430074, China;(2) Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, B-3001 Leuven, Belgium |
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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.
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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Keywords: | Asymptotic stability Neutral multidelay-integro-differential equation Runge– Kutta method Linear multistep method |
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