A new symmetric two-step P-stable Obrechkoff method with 12 algebraic order for the numerical solution of second-order IVPs

A new two-step implicit P-stable Obrechkoff of twelfth algebraic order with vanished phase-lag and its first, second and third derivatives is constructed in this paper. The purpose of this paper is to develop an efficient algorithm for the approximate solution of the second order iniitial value problems that have oscillatory or periodic solutions. This algorithm belongs in the category of the multistep and multiderivative methods. The advantage of the new methods in comparison with similar methods, in terms of efficiency, accuracy and stability, have been showed by the implementation of them in some important problems, including the undamped Duffing equation, etc. -------------- A new two-step implicit P-stable Obrechkoff of twelfth algebraic order with vanished phase-lag and its first, second and third derivatives is constructed in this paper. The purpose of this paper is to develop an efficient algorithm for the approximate solution of the second order iniitial value problems that have oscillatory or periodic solutions. This algorithm belongs in the category of the multistep and multiderivative methods. The advantage of the new methods in comparison with similar methods, in terms of efficiency, accuracy and stability, have been showed by the implementation of them in some important problems, including the undamped Duffing equation, etc.