Analysis of Derivative Free Rational Scheme

Abstract

In this research paper we present analysis of the derivative free rational one step scheme for solving Initial Value problems of first order Ordinary differential Equations (ODEs). The scheme shows to be 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 possesses singularities.