SPECIAL OPTIMIZED RUNGE–KUTTA METHODS FOR IVPsWITH OSCILLATING SOLUTIONS

Z. A. Anastassi and T. E. Simos ()
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Z. A. Anastassi: Department of Computer Science and Technology, Faculty of Sciences and Technology, University of Peloponnese, GR-22 100 Tripolis, Greece
T. E. Simos: Department of Computer Science and Technology, Faculty of Sciences and Technology, University of Peloponnese, GR-22 100 Tripolis, Greece

International Journal of Modern Physics C (IJMPC), 2004, vol. 15, issue 01, 1-15

Abstract: In this paper we present a family of explicit Runge–Kutta methods of 5th algebraic order, one of which has variable coefficients, for the efficient solution of problems with oscillating solutions. Emphasis is placed on the phase-lag property in order to show its importance with regards to problems with oscillating solutions. Basic theory of Runge–Kutta methods, phase-lag analysis and construction of the new methods are described. Numerical results obtained for known problems show the efficiency of the new methods when they are compared with known methods in the literature. Furthermore we note that the method with variable coefficients appears to have much higher accuracy, which gets close to double precision, when the product of the frequency with the step-length approaches certain values. These values are constant and independent of the problem solved and depend only on the method used and more specifically on the expressions used to achieve higher algebraic order.

Keywords: Numerical solution; initial value problems (IVPs); explicit methods; phase-lag; variable coefficients (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1142/S0129183104006510

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