A new higher order effective P–C methods for stiff systems

In this paper a special class of k-step methods of order k+1 with two free parameters up to order 9 are established. The stability analysis of the P–C scheme is investigated. The coefficients of our class and the values of the parameters for getting A0-stable schemes are tabulated. The relation between the parameters for obtaining L(α)-stable formula is determined. A comparison between the stability region and the error estimation for the fourth-order of our scheme and Cash's scheme is carried on.