Improved Extended Runge-Kutta-like Method for Solving First Order IVPs.

In this research, we proposed a family of improved extended Runge-Kutta-like methods which incorporate the function as well as the derivative of the function for the numerical integration of autonomous and non-autonomous ordinary differential equations. The proposed methods are more accurate than the existing methods in the literature and acquire bigger regions of stability. Numerical examples illustrating the computational accuracy are presented and the stability regions are also shown.