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A New Trigonometrically Fitted Two‐Derivative Runge‐Kutta Method for the Numerical Solution of the Schrödinger Equation and Related Problems

Author

Listed:
  • Yanwei Zhang
  • Haitao Che
  • Yonglei Fang
  • Xiong You

Abstract

A new trigonometrically fitted fifth‐order two‐derivative Runge‐Kutta method with variable nodes is developed for the numerical solution of the radial Schrödinger equation and related oscillatory problems. Linear stability and phase properties of the new method are examined. Numerical results are reported to show the robustness and competence of the new method compared with some highly efficient methods in the recent literature.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:937858
    DOI: 10.1155/2013/937858
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    References listed on IDEAS

    as
    1. 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, Hindawi, vol. 2012, pages 1-27, October.
    2. T. E. Simos, 2000. "An Embedded Runge–Kutta Method With Phase-Lag Of Order Infinity For The Numerical Solution Of The Schrödinger Equation," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 11(06), pages 1115-1133.
    3. 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).
    Full references (including those not matched with items on IDEAS)

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    1. Yonglei Fang & Qinghong Li & Qinghe Ming & Kaimin Wang, 2012. "A New Optimized Runge‐Kutta Pair for the Numerical Solution of the Radial Schrödinger Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).

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