Solving Nonlinear Delay-Differential-Algebraic Equations with Singular Perturbation via Block Boundary Value Methods
Year: 2023
Author: Xiaoqiang Yan, Xu Qian, Hong Zhang, Songhe Song, Xiujun Cheng
Journal of Computational Mathematics, Vol. 41 (2023), Iss. 4 : pp. 643–662
Abstract
Block boundary value methods (BBVMs) are extended in this paper to obtain the numerical solutions of nonlinear delay-differential-algebraic equations with singular perturbation (DDAESP). It is proved that the extended BBVMs in some suitable conditions are globally stable and can obtain a unique exact solution of the DDAESP. Besides, whenever the classic Lipschitz conditions are satisfied, the extended BBVMs are preconsistent and $p$th order consistent. Moreover, through some numerical examples, the correctness of the theoretical results and computational validity of the extended BBVMs is further confirmed.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2109-m2021-0020
Journal of Computational Mathematics, Vol. 41 (2023), Iss. 4 : pp. 643–662
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Nonlinear delay-differential-algebraic equations with singular perturbation Block boundary value methods Unique solvability Convergence Global stability.
Author Details
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The extended block generalized Störmer–Cowell methods for second-order nonlinear delay-differential–algebraic equations with index-1
Yan, Xiaoqiang
Chen, Shi
Xiao, Aiguo
Wang, Huiru
Journal of Computational and Applied Mathematics, Vol. 440 (2024), Iss. P.115650
https://doi.org/10.1016/j.cam.2023.115650 [Citations: 0]