Chebyshev–Picard iteration methods for solving delay differential equations

Quan Zhou, Yinkun Wang and Yicheng Liu

Mathematics and Computers in Simulation (MATCOM), 2024, vol. 217, issue C, 1-20

Abstract: 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.

Keywords: Chebyshev–Picard iteration method; Delay differential equation; Feasible iterative interval; Numerical analysis (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:217:y:2024:i:c:p:1-20

DOI: 10.1016/j.matcom.2023.09.023

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