Solving Nonlinear Delay-Differential-Algebraic Equations with Singular Perturbation via Block Boundary Value Methods

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

Xiaoqiang Yan

Xu Qian

Hong Zhang

Songhe Song

Xiujun Cheng

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