A new three stage implicit Runge-Kutta type method with error estimation for first order ordinary differential equations

This paper presents a new three stage implicit Runge-Kutta type method for solving initial value problems of first order ordinary differential equations (ODEs). Collocation approach is used to derive a method of Continuous coefficient system and when evaluated at special Gaussian points gives three different discrete schemes. These schemes were further reformulated to three stage Runge-Kutta type method and when tested with numerical experiments, it demonstrates highly efficient, stable and low implementation cost when compared with existing methods. This scheme can handled both Stiff and non Stiff ODEs.