Accurate solutions of first order nonlinear initial value problems for ordinary differential equations withtherunge - kutta - fehlberg method

This paper applies the fifth order Runge-Kutta-Fehlberg method for solving nonlinear first orderinitial value problem. The proposed method is quite efficient and practically well suited for solving these problems. In order to verify the accuracy, we compare numerical solutions with the exact solutions. The numerical solutions are in good agreement with the exact solutions. The stability analysis of the method has been investigated. Three model examples are given to demonstrate the reliability and efficiency of the methods. The proposed method also compared with some previously existing literatures and shows betterment results.