A Combination of the Orthogonal Polynomials with Least –Squares Method for Solving High-Orders Fredholm-Volterra Integro-Differential Equations

Hameeda Oda Al-Humedi, Department Mathematics, Education College for Pure Sciences, Basrah University, Basrah, IraqFollow
Ahsan Fayez Shoushan, Department Mathematics, Education College for Pure Sciences, Basrah University, Basrah, IraqFollow

Document Type

Article

Abstract

This study introduced new technique which is based on a combination of the least-squares technique (LST) with Chebyshev and Legendre polynomials for finding the approximate solutions of higher-order linear Fredholm-Volterra integro-differential equations (FVIDEs) subject to the mixed conditions. Two examples of second and third-order linear FVIDEs are considered to illustrate the proposed method, the numerical results are comprised to demonstrate the validity and applicability of this technique, and comparisons with the exact solution are made. These results have shown that the competence and accuracy of the present technique.

Keywords

Fredholm-Volterra Integro-Differential equations, Chebyshev and Legendre polynomials

Recommended Citation

Al-Humedi, Hameeda Oda and Shoushan, Ahsan Fayez (2021) "A Combination of the Orthogonal Polynomials with Least –Squares Method for Solving High-Orders Fredholm-Volterra Integro-Differential Equations," Al-Qadisiyah Journal of Pure Science: Vol. 26 : No. 1 , Article 3.
Available at: https://doi.org/10.29350/qjps.2021.26.1.1207