A highly efficient implicit Runge-Kutta method for first order ordinary differential equations

In this paper we develop a more efficient three-stage implicit Runge-Kutta method of order 6 for solving first order initial value problems of ordinary differential equations. Collocation method is used to derive Continuous schemes in which both the interpolation and collocation points are at perturbed Gaussian points. This gives a higher order scheme, which is more efficient and stable than the existing similar ones. Simple linear problems are used to check its level of accuracy and stability.   Key words: Implicit, more efficient, stable, collocation methods, Perturbed Gaussian points and error estimates.