2023/03/04 by Kazeem Issa, Issa, Kazeem, Kazeem Aliu +5
Mathematics · Physics and Astronomy · #Differential Equations and Numerical Methods #Fractional Differential Equations Solutions #Fredholm equation #Nonlinear Waves and Solitons #Orthogonal polynomials #Perturbation terms #Volterra equation
paper · doi:10.82521/ijo.2023.1018879
openalex publication_date 2023/03/04 · openalex created_date 2025/12/27 · openalex updated_date 2026/07/07
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.