Analysis of Derivative Free Rational Scheme

In this research paper we present analysis of the derivative free rational one step scheme for solving initial value problems (IVPs) of first order Ordinary differential Equations (ODEs). The scheme is consistent and stability property resembles of the trapezoidal method, which is A-stable. This method has been applied to problems with singularities and the one which are considered to be stiff. Numerical results show that the scheme is suitable for solving both stiff problems and the one whose solutions possess singularities.