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

Subject Areas : Statistics

ali shokri ¹ (Department of Mathematics, Faculty of Basic Science, University of Maragheh, Maragheh, Iran)
abbas-ali shokri ² (Department of Mathematics, Ahar Branch, Islamic Azad University-Ahar-Iran)
Mohammad Mehdizadeh Khalsarei ³ (Department of Mathematics, Faculty of Science, University of Maragheh, Maragheh,Iran)
firoz pashaie ⁴ (Department of Mathematics, Faculty of Science, University of Maragheh, Maragheh,Iran)

Received: 2018-10-12 Accepted : 2020-02-27 Published : 2020-12-21

Keywords: روش های چندمشتقی, مسائل مقدار اولیه, ناحیه پایداری, فاز تاخیری,

Abstract :

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.

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