An efficient numerical algorithm for solving delay differential equations based on second kind Chebyshev polynomials
Source abstract
Abstract
This paper proposes a fast spectral technique based on second kind Chebyshev polynomials (SKCPs) to numerically solve delay differential equations (DDEs). First, we introduce some features of the SKCPs. Then, we use the operational matrices of coefficients, derivation, and stretch of the shifted SKCPs to convert DDEs into systems of algebraic equations. We show that these matrices are sparse, allowing for a fast implementation of the numerical calculations. A theoretical discussion about error estimation is conducted, and finally, numerical examples are given to highlight the accuracy and efficiency of the proposed method.
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Research context
OpenAlex topics: Fractional Differential Equations Solutions · Numerical methods for differential equations · Mathematical functions and polynomials
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Department of Mathematics, Karaj Branch, Islamic Azad University 1 , Karaj 31499-68111,
Department of Mathematics, College of Education, Misan University 2 , Misan 62001,
Department of Mathematics, Velayat University 3 , Iranshahr,
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