New process to approach linear Fredholm integral equations defined on large interval

Abstract

To tackle a linear Fredholm integral equation on great interval, two numerical processes are involved: discretization and iterative scheme. The conventional numerical process is discretize first then use an iterative scheme as Jacobi’s method to approach the solutions of the huge algebraic system. In this paper, we propose an alternative numerical process, we apply an iterative scheme based on construction of a generalization of the iterative scheme for Jacobi method which is adapted to the system of linear bounded operators, then we use Nyström method to discretize only the diagonal part of the system. The convergence analysis of this new method is proved and numerical tests developed show its effectiveness.