High performance of the Remez algorithm in ﬁnding polynomial approximations for the solution of integral equations

	High performance of the Remez algorithm in ﬁnding polynomial approximations for the solution of integral equations
International Journal of Nonlinear Analysis and Applications
مقاله 168، دوره 14، شماره 1، فروردین 2023، صفحه 2129-2142 اصل مقاله (850.91 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2020.19851.2109
نویسنده
Ali Darijani^*
Department of Mathematics, Higher Education Complex of Bam, Bam, Iran.
چکیده
In this paper, the solution of the general integral equation of the second kind is approximated using polynomials. These polynomials are obtained based on the Remez algorithm and the minimization of residual function. The nature of the use of the Remez algorithm in the proposed method will lead to the conversion of the integral equation to a system of algebraic equations and obtaining the best polynomial approximation for the solution of an integral equation. Also, the convergence analysis of the approach is discussed. Finally, some numerical examples and comparisons with previous results confirm the efficiency and high accuracy of the presented method.
کلیدواژه‌ها
Nonlinear integral equations؛ Remez algorithm؛ Best polynomial approximation؛ Residual function؛ Minimization؛ Inﬁnity norm
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