Numerical Solutions of Second Order Initial Value Problems of Bratu-Type equation Using Higher Ordered Rungu-Kutta Method

Abstract

This paper presents the fifth order Runge-Kutta method (RK5) to find the numerical solution of the second order initial value problems of Bratu-type ordinary differential equations. In order to justify the validity and effectiveness of the method, we solve three model examples and compare the exact solutions to numerical solutions. The numerical results in terms of point wise absolute errors presented in tables and the plotted graphs show that the present method approximates the exact solution very well. Besides, the stability of the method had been checked and verified.