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

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SHOKRI ALI; SHOKRI ABBAS ALI; Mehdizadeh Khalsarei Mohammad; Pashaie Firoz

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Journal: JOURNAL OF NEW RESEARCHES IN MATHEMATICS Year:2022 | Volume:6 | Issue:27 Page(s): 127-139

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Title

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

Author(s)

SHOKRI ALI | SHOKRI ABBAS ALI | Mehdizadeh Khalsarei Mohammad | Pashaie Firoz | Issue Writer Certificate

Keywords

Stability region

Phase-lag

Initial value problems

Moltiderivative methods

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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APA: Copy

SHOKRI, ALI, SHOKRI, ABBAS ALI, Mehdizadeh Khalsarei, Mohammad, & Pashaie, Firoz. (2022). A new symmetric two-step P-stable Obrechkoff method with 12 algebraic order for the numerical solution of second-order IVPs. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, 6(27 ), 127-139. SID. https://sid.ir/paper/950765/en

Vancouver: Copy

SHOKRI ALI, SHOKRI ABBAS ALI, Mehdizadeh Khalsarei Mohammad, Pashaie Firoz. A new symmetric two-step P-stable Obrechkoff method with 12 algebraic order for the numerical solution of second-order IVPs. JOURNAL OF NEW RESEARCHES IN MATHEMATICS[Internet]. 2022;6(27 ):127-139. Available from: https://sid.ir/paper/950765/en

IEEE: Copy

ALI SHOKRI, ABBAS ALI SHOKRI, Mohammad Mehdizadeh Khalsarei, and Firoz Pashaie, “A new symmetric two-step P-stable Obrechkoff method with 12 algebraic order for the numerical solution of second-order IVPs,” JOURNAL OF NEW RESEARCHES IN MATHEMATICS, vol. 6, no. 27 , pp. 127–139, 2022, [Online]. Available: https://sid.ir/paper/950765/en

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