Numerical Treatment of Volterra integral Equation of the 2nd kind Using 6thorder of Runge-Kutta method

Abstract

The aim of this paper is to study and to obtain an approximate solution of non-linear Volterra integral equation of the second kind ,the researcher implemented the modified method by using specific examples involving volterra integral equation to show the capability and efficiency of our approximate method according to the exact solution in addition to the ease in programming the approximate method Keywords: General 2 nd order of non-linear Volterra integral equation, 6 th order Improved Range-Kutta methods. ________________________________________________________________________________________________________ 2-DEFINITION OF VOLTERRA INTEGRAL EQUATIONSThe general form of volterra integral equation is given by the form