Numerical solution of integro-differential equations via pertubed-Gegenbauer, Jacobi polynomials and Galerkin method

Iranian Journal of Optimization

دوره 15، شماره 1، خرداد 2023

نوع مقاله: Research Paper

نویسندگان

Kazeem Issa^{* 1}؛ Tajudeen Aliu²؛ Ruth Arokoola³؛ Oluwatumininu Micah³

¹Department of Mathematics and Statistics, Kwara State University, Malete Nigeria PMB 1530, Ilorin Nigeria

²Department of Mathematics and Statistics, Kwara State University

³Kwara State University

چکیده

In this paper, we proposed perturbed Galerkin method for solving integro-differential equations via shifted Gegenbauer and shifted Jacobi polynomials as approximating polynomials. We use Galerkin method to transform the perturbed integro-differential equation to system of linear algebraic equations and obtained N + 1 linear equations with N +m+2 unknowns. Moreover, with m+1 boundary conditions we obtained N +m+2 algebraic equations which was then solved to obtain the approximate solutions at various values of α and β depending on the orthogonal polynomials, that’s shifted Gegenbauer or shifted Jacobi polynomials. The proposed method was implemented on some selected problems in the literature to validate the effectiveness and the accuracy of the proposed method.

کلیدواژه‌ها

Perturbation terms؛ Orthogonal polynomials؛ Volterra equation؛ Fredholm equation