Chebyshev-Picard iteration methods for solving delay differential equations

被引：2

作者：

Zhou, Quan ^{[1
]}

Wang, Yinkun ^{[1
]}

Liu, Yicheng ^{[1
]}

机构：

[1] Natl Univ Def Technol, Coll Sci, Changsha 410073, Hunan, Peoples R China

来源：

MATHEMATICS AND COMPUTERS IN SIMULATION | 2024年 / 217卷

基金：

中国国家自然科学基金;

关键词：

Chebyshev-Picard iteration method; Delay differential equation; Feasible iterative interval; Numerical analysis; LINEAR MULTISTEP METHODS; COLLOCATION METHODS; NUMERICAL-SOLUTION; STABILITY;

D O I：

10.1016/j.matcom.2023.09.023

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

In this paper, we propose an effective Chebyshev-Picard iteration (CPI) method for solving delay differential equations with a constant delay. This approach adopts the Chebyshev series to represent the solution and improves the accuracy of the solution by successive Picard iterations. The CPI method is implemented in a matrix-vector form efficiently without matrix inversion. We also present a multi-interval CPI method for solving long-term simulation problems. Further, the convergence of the CPI method is analyzed by evaluating the eigenvalues of the coefficient matrices of the iteration. Several numerical experiments including both the linear and nonlinear systems with delay effects are presented to demonstrate the high accuracy and efficiency of the CPI method by comparison with the classic methods.(c) 2023 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

引用

页码：1 / 20

页数：20

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