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; Geoffrey Kumlengand; Joshua Sunday (Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang, 2020)
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.