A Computational Block Method with Five Hybrid-Points for Differential Equations Containing a Piece-wise Constant Delay

This paper presents an efficient numerical approach for first-order delay differential equations containing a piece-wise constant delay. The strategy is based on a five-point hybrid block method that has been developed for ordinary differential equations. We will use the interpolation technique for...

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Bibliographic Details
Published inDifferential equations and dynamical systems Vol. 33; no. 1; pp. 1 - 14
Main Authors Bisheh-Niasar, Morteza, Ramos, Higinio
Format Journal Article
LanguageEnglish
Published New Delhi Springer India 01.01.2025
Subjects
Computer Science
Engineering
Mathematics
Mathematics and Statistics
Original Research
Zero stability
Piece-wise constant delay differential equations
Block method
Consistency
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Summary:This paper presents an efficient numerical approach for first-order delay differential equations containing a piece-wise constant delay. The strategy is based on a five-point hybrid block method that has been developed for ordinary differential equations. We will use the interpolation technique for the evaluation of delay terms that are not defined at the grid points. The main characteristics are discussed, including zero stability, local truncation errors, convergence and stability region. The method is easy to implement, and the numerical experiments show the efficiency and accuracy of the proposed method, compared to other methods appeared in the literature.
ISSN:0971-3514
0974-6870
DOI:10.1007/s12591-022-00624-9