Numerical Solutions of Nonlinear Fredholm Integro Differential Equations using Fifth Order Runge-kutta Method

Abstract

This paper is considered with the numerical solution of a type of second-order nonlinear Fredholm integro-differential Equations (FIDs). The proposed scheme is based on Runge - kutta methods of order fifth. Moreover, two numerical examples are considered to show the capability and the accuracy of the proposed methods compared with other Runge-kutta methods of less order. Finally, we apply the least square errors (LSE) formula to make numerical comparisons between the numerical and the exact solutions. The obtained results show that the proposed method is superior and more accurate than Runge - kutta methods of orders two, three, and four.