Numerical Solution of Second Order Initial Value Problems of Bratu-type Equations using Sixth Order Runge-Kutta Seven Stages Method

In this paper, second order initial value problem of Bratu-type ordinary differential equations is solved numerically using sixth order Runge-Kutta seven stages method. The stability of the method is checked and verified. In order to justify the validity and effectiveness of the method, two model examples are solved and the numerical solutions are compared to the corresponding exact solutions. Furthermore, the results obtained using the current method are compared with the numerical results obtained by other researchers. The numerical results in terms of point-wise absolute errors presented in tables and plotted graphs show that the present method approximates the exact solutions very well.