Application of newton-gs iteration with quadrature scheme to solve nonlinear Fredholm integral equations

This paper presents the application of Newton Gauss-Seidel (Newton-GS) iteration with the first-order quadrature scheme to solve nonlinear Fredholm integral equations of second kind (NFIE-2). By using first-order quadrature scheme, a system of nonlinear Fredholm integral equation can be generated. Actually, Newton-GS iteration is based on the combination of Newton’s method and Gauss Seidel iteration. Based on this combination, this Newton’s method is used to linearize the generated system of nonlinear system to a linear system and then solved it iteratively by using Gauss-Seidel iteration. To illustrate the effectiveness of the Newton-GS method, the numerical experiments have been conducted by comparing the results with Newton-Jacobi. Referring to three main criteria of comparison, which is number of iteration, iteration time and maximum absolute error. The comparative results show that Newton-GS is superior to Newton-Jacobi.