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 - <p style="text-align: justify;">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.</p>