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

Authors

  • Xiaoqiang Yan College of Liberal Arts and Sciences, National University of Defense Technology, Changsha 410073, China
  • Xu Qian College of Liberal Arts and Sciences, National University of Defense Technology, Changsha 410073, China
  • Hong Zhang College of Liberal Arts and Sciences, National University of Defense Technology, Changsha 410073, China
  • Songhe Song College of Liberal Arts and Sciences, National University of Defense Technology, Changsha 410073, China
  • Xiujun Cheng College of Science, Zhejiang Sci-Tech University, Hangzhou 310018, China

DOI:

https://doi.org/10.4208/jcm.2109-m2021-0020

Keywords:

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

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.

Downloads

Published

2023-04-25

Issue

Vol. 41 No. 4 (2023)

Section

Articles