University of KashanIranian Journal of Mathematical Chemistry2228-64896220151001Trigonometrically fitted two-step obrechkoff methods for the numerical solution of periodic initial value problems1451611045110.22052/ijmc.2015.10451ENA. ShokriDepartment of Mathematics, Faculty of Basic Science, University of Maragheh, Maragheh, Iran.A. A.ShokriDepartment of Mathematics, Ahar Branch, Islamic Azad University, Ahar, Iran.Sh. MostafaviFaculty of Mathematical Science, University of Maragheh, Maragheh, Iran.H. SaadatDepartment of Mathematics, Faculty of Basic Science, University of Maragheh, Maragheh, IranJournal Article20140518In 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.http://ijmc.kashanu.ac.ir/article_10451_e37900e24a74b6f240f6b1f76209f4e0.pdf