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A New Approximation Method for Multi-Pantograph Type Delay Differential Equations Using Boubaker Polynomials

Şuayip Yüzbaşı

https://orcid.org/0000-0002-5838-7063

Department of Mathematics, Faculty of Science, Bartin University, Tr-74100, Bartin, Turkey

E-mail Address: suayipyuzbasi@gmail.com

E-mail Address: suayipyuzbasi@bartin.edu.tr

Corresponding author.

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Beyza Çetin

https://orcid.org/0000-0002-0059-5855

Department of Mathematics, Faculty of Science, Akdeniz University, Antalya, Turkey

E-mail Address: beyzaccetinn@gmail.com

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https://doi.org/10.1142/S0219876223500342Cited by:1 (Source: Crossref)

Abstract

In this paper, a new approaching technique is offered to unravel multi-pantograph-type delay differential equations. The suggested new method is a collocation method based on integration and Boubaker polynomials. As the main idea of the method, the process starts by approaching the first derivative function in the equation in the form of truncated Boubaker series. Then this approximating form is composed in the matrix form. The unknown function is then obtained by integrating the approximate derivative function and expressing it as a matrix. Using the approximation, the matrix forms for the proportionally delayed terms in the equation are derived. In addition, operational matrix forms are constructed for convenience in the method. By using these matrix forms and matrix operations, the problem is reduced to a system of algebraic linear equations. The method is illustrated through numerical implementations and compared with existing techniques in the literature. The results demonstrate the effectiveness and reliability of the proposed approach, highlighting its superiority over other methods.

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