Modified THDRK methods for the numerical integration of the Schrödinger equation

Yonglei Fang (), Yanping Yang (), Xiong You and Lei Ma ()
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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

International Journal of Modern Physics C (IJMPC), 2020, vol. 31, issue 10, 1-11

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.

Keywords: Three-derivative Runge–Kutta method; Schrödinger equation; error analysis; Woods–Saxon potential (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1142/S0129183120501491

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