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A New Family of Phase‐Fitted and Amplification‐Fitted Runge‐Kutta Type Methods for Oscillators

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Listed:
  • Zhaoxia Chen
  • Xiong You
  • Xin Shu
  • Mei Zhang

Abstract

In order to solve initial value problems of differential equations with oscillatory solutions, this paper improves traditional Runge‐Kutta (RK) methods by introducing frequency‐depending weights in the update. New practical RK integrators are obtained with the phase‐fitting and amplification‐fitting conditions and algebraic order conditions. Two of the new methods have updates that are also phase‐fitted and amplification‐fitted. The linear stability and phase properties of the new methods are examined. The results of numerical experiments on physical and biological problems show the robustness and competence of the new methods compared to some highly efficient integrators in the literature.

Suggested Citation

  • Zhaoxia Chen & Xiong You & Xin Shu & Mei Zhang, 2012. "A New Family of Phase‐Fitted and Amplification‐Fitted Runge‐Kutta Type Methods for Oscillators," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:236281
    DOI: 10.1155/2012/236281
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    References listed on IDEAS

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    1. T. E. Simos & Jesus Vigo Aguiar, 2001. "A Symmetric High Order Method With Minimal Phase-Lag For The Numerical Solution Of The Schrödinger Equation," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 12(07), pages 1035-1042.
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    Cited by:

    1. Yanwei Zhang & Haitao Che & Yonglei Fang & Xiong You, 2013. "A New Trigonometrically Fitted Two‐Derivative Runge‐Kutta Method for the Numerical Solution of the Schrödinger Equation and Related Problems," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).

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