Numerical treatment of the nonlinear Volterra integral equation by Newton-Kantorovich method

Abstract

Many problems which arise in mathematical physics, engineering, biology, economics,...etc., lead to mathematical models described by nonlinear integral equation. In this work, the aim is solve numerically the nonlinear Volterra integral equation by the combination of Newton Kantorovich method with modiÖed Simpson method.This method transforms the nonlinear integral equation to a linear integral equation of the second kind which be solve by the modiÖed Simpson method.