Abstract.

This paper presents new two-step explicit symmetric P-stable methods, including Obrechkoff and hybrid terms, of orders four and six for solving initial value problems of second order ordinary dfferential equations. In this paper, we improved the method written by Xinyuan Wu and Qinghong Li [11], in a way that we could increase order and accuracy of their methods. The numerical results obtained by the new methods on some IVPs equations show the superior efficiency, accuracy, stability of the methods presented in this paper.

Keywords:

hybrid methods, P-stable, off-step points, Obrechkoff methods.