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Phase-Fitted and Amplification-Fitted Higher Order Two-Derivative Runge-Kutta Method for the Numerical Solution of Orbital and Related Periodical IVPs

Author

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  • N. A. Ahmad
  • N. Senu
  • F. Ismail

Abstract

A phase-fitted and amplification-fitted two-derivative Runge-Kutta (PFAFTDRK) method of high algebraic order for the numerical solution of first-order Initial Value Problems (IVPs) which possesses oscillatory solutions is derived. We present a sixth-order four-stage two-derivative Runge-Kutta (TDRK) method designed using the phase-fitted and amplification-fitted property. The stability of the new method is analyzed. The numerical experiments are carried out to show the efficiency of the derived methods in comparison with other existing Runge-Kutta (RK) methods.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jnlmpe:1871278
    DOI: 10.1155/2017/1871278
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    Cited by:

    1. Athinoula A. Kosti & Simon Colreavy-Donnelly & Fabio Caraffini & Zacharias A. Anastassi, 2020. "Efficient Computation of the Nonlinear Schrödinger Equation with Time-Dependent Coefficients," Mathematics, MDPI, vol. 8(3), pages 1-12, March.
    2. Zacharias A. Anastassi & Athinoula A. Kosti & Mufutau Ajani Rufai, 2023. "A Parametric Method Optimised for the Solution of the (2+1)-Dimensional Nonlinear Schrödinger Equation," Mathematics, MDPI, vol. 11(3), pages 1-17, January.
    3. 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.

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