Trigonometrically Fitted Two-step Obrechkoff Methods for the Numerical Solution of Periodic Initial Value Problems

Shokri, A.; Shokri, A. A.; Mostafavi, Sh.; Saadat, H.

doi:10.22052/ijmc.2015.10451

Trigonometrically Fitted Two-step Obrechkoff Methods for the Numerical Solution of Periodic Initial Value Problems

Document Type : Research Paper

Authors

A. Shokri ¹

A. A. Shokri ²

Sh. Mostafavi ³

H. Saadat ⁴

¹ Department of Mathematics, Faculty of Basic Science, University of Maragheh, Maragheh, Iran.

² Department of Mathematics, Ahar Branch, Islamic Azad University, Ahar, Iran.

³ Faculty of Mathematical Science, University of Maragheh, Maragheh, Iran.

⁴ Department of Mathematics, Faculty of Basic Science, University of Maragheh, Maragheh, Iran

10.22052/ijmc.2015.10451

Abstract

In this paper, we present a new two-step trigonometrically fitted symmetric Obrechkoff method. The method is based on the symmetric two-step Obrechkoff method, with eighth algebraic order, high phase-lag order and is constructed to solve IVPs with periodic solutions such as orbital problems. We compare the new method to some recently constructed optimized methods from the literature. The numerical results obtained by the new method for some problems show its superiority in efficiency, accuracy and stability.

Keywords

Obrechkoff methods

Trigonometrically-fitting

Initial value problems

Symmetric multistep methods

Oscillating solution

Subjects