14 New Improved Runge-Kutta Method with Reducing Number of Function Evaluations

The set of explicit third-order New Improved Runge-Kutta (NIRK) method that just uses two function evaluations per step is developed. Because of lower number of function evaluations, the scheme proposed herein has a lower computational cost than the classical third-order Runge-Kutta method while maintaining the same order of local accuracy. The stability region of the new method are discussed also the numerical examples are presented to illustrate the computational efficiency and accuracy for the new method.