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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.

Yan , XiaoqiangQian , XuZhang , HongSong , Songhe and Cheng , Xiujun. (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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