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Volume 41, Issue 4
Solving Nonlinear Delay-Differential-Algebraic Equations with Singular Perturbation via Block Boundary Value Methods

Xiaoqiang Yan, Xu Qian, Hong Zhang, Songhe Song & Xiujun Cheng

DOI: 10.4208/jcm.2109-m2021-0020

J. Comp. Math., 41 (2023), pp. 643-662.

Published online: 2023-02

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  • 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.

  • Keywords

Nonlinear delay-differential-algebraic equations with singular perturbation, Block boundary value methods, Unique solvability, Convergence, Global stability.

  • AMS Subject Headings

34K50, 60H35, 65L80, 65L20

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

xqyan1992@xtu.edu.cn (Xiaoqiang Yan)

qianxu@nudt.edu.cn (Xu Qian)

zhanghnudt@163.com (Hong Zhang)

shsong@nudt.edu.cn (Songhe Song)

xiujuncheng@zstu.edu.cn (Xiujun Cheng)

  • BibTex
  • RIS
  • TXT
@Article{JCM-41-643, author = {Yan , XiaoqiangQian , XuZhang , HongSong , Songhe and Cheng , Xiujun}, title = {Solving Nonlinear Delay-Differential-Algebraic Equations with Singular Perturbation via Block Boundary Value Methods}, journal = {Journal of Computational Mathematics}, year = {2023}, volume = {41}, number = {4}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2109-m2021-0020}, url = {http://global-sci.org/intro/article_detail/jcm/21409.html} }
TY - JOUR T1 - Solving Nonlinear Delay-Differential-Algebraic Equations with Singular Perturbation via Block Boundary Value Methods AU - Yan , Xiaoqiang AU - Qian , Xu AU - Zhang , Hong AU - Song , Songhe AU - Cheng , Xiujun JO - Journal of Computational Mathematics VL - 4 SP - 643 EP - 662 PY - 2023 DA - 2023/02 SN - 41 DO - http://doi.org/10.4208/jcm.2109-m2021-0020 UR - https://global-sci.org/intro/article_detail/jcm/21409.html KW - Nonlinear delay-differential-algebraic equations with singular perturbation, Block boundary value methods, Unique solvability, Convergence, Global stability. AB -

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.

Xiaoqiang Yan, Xu Qian, Hong Zhang, Songhe Song & Xiujun Cheng. (2023). Solving Nonlinear Delay-Differential-Algebraic Equations with Singular Perturbation via Block Boundary Value Methods. Journal of Computational Mathematics. 41 (4). 643-662. doi:10.4208/jcm.2109-m2021-0020
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