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Modified THDRK methods for the numerical integration of the Schrödinger equation

Author

Listed:
  • Yonglei Fang

    (School of Mathematics and Statistics, Zaozhuang University, Zaozhuang 277160, P. R. China)

  • Yanping Yang

    (School of Mathematics and Statistics, Zaozhuang University, Zaozhuang 277160, P. R. China)

  • Xiong You

    (Department of Applied Mathematics, Nanjing Agricultural University, Nanjing 210095, P. R. China)

  • Lei Ma

    (School of Optoelectronic Engineering, Zaozhuang University, Zaozhuang 277160, P. R. China)

Abstract

Modified three-derivative Runge–Kutta (MTHDRK) methods for the numerical solution of the resonant state for the Schrödinger equation are investigated. Order conditions are presented and oscillation-fitting conditions are derived. Two practical fifth-order explicit MTHDRK methods are constructed and the error analysis is carried out for large energy. The numerical results are presented for the numerical solution of the Schrödinger equation to show the robustness of our new methods.

Suggested Citation

  • Yonglei Fang & Yanping Yang & Xiong You & Lei Ma, 2020. "Modified THDRK methods for the numerical integration of the Schrödinger equation," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 31(10), pages 1-11, October.
    • Handle: RePEc:wsi:ijmpcx:v:31:y:2020:i:10:n:s0129183120501491
    DOI: 10.1142/S0129183120501491
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    Cited by:

    1. 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.

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