Numerical Solution of Volterra Integro–Differential Equation Using 6th Order Runge-Kutta Method

Abstract

Abstract In this paper, a 6th order Runge-Kutta with seven stages method for finding the numerical solution of Volterra integro-differential equation is considered. The integral term in the Volterra integro-differential equation approximated using the Lagrange interpolation numerical method is discussed. Some illustrative examples are presented to illustrate the accuracy and efficiency of the method and the results are compared with the 5th order Runge-Kutta-Fehlberg and the Improved Runge-Kutta of the 5th order method, Tables and Figures are provided to demonstrate the validity and applicability of the method as well as the approximate accuracy of results. All numerical calculations in this paper have been carried out with MATLAB.