A new two-step P-stable hybrid Obrechkoff method for the numerical integration of second-order IVPs

In this paper, we introduce a class of new P-stable hybrid Obrechkoff methods for the numerical solution of second-order initial value problems. We generate a two-step, symmetric, P-stable hybrid Obrechkoff method of order 8 with two off-step, symmetric, points and phase lag of order at least 2 and for special cases, this order can be increased up to 6. The numerical results obtained by the new method for some problems show its superiority in efficiency, accuracy and stability.