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Convergence and stability of extended BBVMs for nonlinear delay-differential-algebraic equations with piecewise continuous arguments

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Abstract

Delay-differential-algebraic equations have been widely used to model some important phenomena in science and engineering. Since, in general, such equations do not admit a closed-form solution, it is necessary to solve them numerically by introducing suitable integrators. The present paper extends the class of block boundary value methods (BBVMs) to approximate the solutions of nonlinear delay-differential equations with algebraic constraint and piecewise continuous arguments. Under the classical Lipschitz conditions, convergence and stability criteria of the extended BBVMs are derived. Moreover, a couple of numerical examples are provided to illustrate computational effectiveness and accuracy of the methods.

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Funding

This work is supported by NSFC (Grant No. 11971010).

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Authors and Affiliations

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

    Chengjian Zhang & Xiaoqiang Yan

  2. Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan, 430074, China

    Chengjian Zhang & Xiaoqiang Yan

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  1. Chengjian Zhang
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  2. Xiaoqiang Yan
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Correspondence to Chengjian Zhang.

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Zhang, C., Yan, X. Convergence and stability of extended BBVMs for nonlinear delay-differential-algebraic equations with piecewise continuous arguments. Numer Algor 87, 921–937 (2021). https://doi.org/10.1007/s11075-020-00993-8

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