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On fitted modifications of Runge–Kutta–Nyström pairs

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  • Tsitouras, Ch.

Abstract

Modification of only four coefficients of the standard Runge–Kutta–Nyström pairs is enough for producing a method of the same orders that integrates exactly the harmonic oscillator as model problem. These new coefficients are O(λ2) perturbations of the initial ones, with λ the frequency of the problem. Theoretical investigation for the possibilities of order reduction is given. Numerical results over standard pairs of orders 6(4) and 8(6) justify our efforts.

Suggested Citation

  • Tsitouras, Ch., 2014. "On fitted modifications of Runge–Kutta–Nyström pairs," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 416-423.
    • Handle: RePEc:eee:apmaco:v:232:y:2014:i:c:p:416-423
    DOI: 10.1016/j.amc.2014.01.069
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    References listed on IDEAS

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    1. Ch. TSITOURAS, 2006. "Explicit Eighth Order Two-Step Methods With Nine Stages For Integrating Oscillatory Problems," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 17(06), pages 861-876.
    2. G. Papageorgiou & Ch. Tsitouras & I. Th. Famelis, 2001. "EXPLICIT NUMEROV TYPE METHODS FOR SECOND ORDER IVPsWITH OSCILLATING SOLUTIONS," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 12(05), pages 657-666.
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    Keywords

    Oscillatory problems; Harmonic oscillator;

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