Most mathematical formulation of physical and biological phenomena often leads to ordinary differential equations of the form

In this study, we propose a one-step numerical scheme that can solve some of these problems and systems of ordinary different equations. Both Matlab and Mathematica have been used to implement our new method. The derivation of the scheme is based on interpolating functions.

The efficiency of the method is examined in terms of consistency, stability and convergence. We also construct the region of absolute stability (RAS) of the scheme.

ordinary differential equations, interpolating functions, region of absolute stability.