An approach of extrapolation methods for the solution of nonlinear Volterra–Fredholm integral equations of the second kind

Abstract

This study presents the process of using extrapolation methods to solve the nonlinear Volterra–Fredholm integral equations of the second kind. To do this, by approximating the integral terms contained in equations by a quadrature rule, the nonlinear Volterra–Fredholm integral equations of the second kind are reduced to a set of nonlinear algebraic equations. Then, the solution of the corresponding system of nonlinear equations is approxi-mated by an iterative method, and finally, these iterations are accelerated by an extrapolation method. We demonstrate the effectiveness of the pro-posed approach by solving some numerical examples.

Keywords

• volterra–fredholm integral equations
• extrapolation methods
• iterative methods