Hybrid BDF with two off-step points for stiff initial value problems

In this paper, we present the details of hybrid methods which are based on backward differenti- ation formula (BDF) for the numerical solution of ordinary differential equations (ODEs). In these hybrid BDF, which are considered from general linear methods point of view, two additional off-step points have been used in the rst derivative of the solution to improve the absolute stability regions. The constructed methods are A(α)-stable up to order 9 so that, as it is shown in the numerical experiments, they are superior for stiff systems.