THE NEW ONE-STEP L-STABLE HYBRID OBRECHKOFF METHODS FOR THE NUMERICAL SOLUTION OF FIRST ORDER IVP’S

In this paper, a class of new one-step, implicit, L-stable hybrid Obrechkoff methods for the numerical solving of first order initial value problems are presented. In this methods, both classes of Obrechkoff and hybrid methods for solving IVP’s are used and derived the new class of hybrid Obrechkoff methods. The numerical results obtained by the new method for some problems show the superiority in efficiency, accuracy and stability.