Construction of an optimized explicit Runge-Kutta-Nyström method for the numerical solution of oscillatory initial value problems

Authors:
A. A. Kosti;Z. A. Anastassi;T. E. Simos
Affiliations:
Laboratory of Computer Sciences, Department of Computer Science and Technology, Faculty of Sciences and Technology, University of Peloponnese, GR-22 100 Tripolis, Greece;Department of Sciences, School of Pedagogical & Technological Education (ASPETE), N.Heraklion, GR-14121 Athens, Greece;Department of Mathematics, College of Sciences, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia and Laboratory of Computer Sciences, Department of Computer Science and Technology, ...
Venue:
Computers & Mathematics with Applications
Year:
2011

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Abstract

An explicit optimized Runge-Kutta-Nystrom method with four stages and fifth algebraic order is developed. The produced method has variable coefficients with zero phase-lag, zero amplification factor and zero first derivative of the amplification factor. We provide an analysis of the local truncation error of the new method. We also measure the efficiency of the new method in comparison to other numerical methods through the integration of the two-body problem with various eccentricities and three other periodical/oscillatory initial value problems.