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High Order Two-Derivative Runge-Kutta Methods with Optimized Dispersion and Dissipation Error

Author

Listed:
  • Theodoros Monovasilis

    (Department of Economics, University of Western Macedonia, 501 00 Kozani, Greece
    These authors contributed equally to this work.)

  • Zacharoula Kalogiratou

    (Department of Informatics, University of Western Macedonia, 501 00 Kozani, Greece
    These authors contributed equally to this work.)

Abstract

In this work we consider explicit Two-derivative Runge-Kutta methods of a specific type where the function f is evaluated only once at each step. New 7th order methods are presented with minimized dispersion and dissipation error. These are two methods with constant coefficients with 5 and 6 stages. Also, a modified phase-fitted, amplification-fitted method with frequency dependent coefficients and 5 stages is constructed based on the 7th order method of Chan and Tsai. The new methods are applied to 4 well known oscillatory problems and their performance is compared with the methods in that of Chan and Tsai.The numerical experiments show the efficiency of the derived methods.

Suggested Citation

  • Theodoros Monovasilis & Zacharoula Kalogiratou, 2021. "High Order Two-Derivative Runge-Kutta Methods with Optimized Dispersion and Dissipation Error," Mathematics, MDPI, vol. 9(3), pages 1-11, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:3:p:232-:d:486460
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    References listed on IDEAS

    as
    1. N. A. Ahmad & N. Senu & F. Ismail, 2017. "Phase-Fitted and Amplification-Fitted Higher Order Two-Derivative Runge-Kutta Method for the Numerical Solution of Orbital and Related Periodical IVPs," Mathematical Problems in Engineering, Hindawi, vol. 2017, pages 1-11, February.
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