Matrix Approach To The Direct Computation Method For The Solution of Fredholm Integro-Differential Equations of The Second Kind With Degenerate Kernels

Nathaniel Mahwash Kamoh (University of Jos)
Geoffrey Kumlengand (University of Jos)
Joshua Sunday (University of Jos)

CAUCHY: Jurnal Matematika Murni dan Aplikasi
Vol 6, No 3 (2020): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI

In this paper, a matrix approach to the direct computation method for solving Fredholm integro-differential equations (FIDEs) of the second kind with degenerate kernels is presented. Our approach consists of reducing the problem to a set of linear algebraic equations by approximating the kernel with a finite sum of products and determining the unknown constants by the matrix approach. The proposed method is simple, efficient and accurate; it approximates the solutions exactly with the closed form solutions. Some problems are considered using maple programme to illustrate the simplicity, efficiency and accuracy of the proposed method.