EXPONENTIALLY FITTED TWO-DERIVATIVE RUNGE–KUTTA METHODS FOR THE SCHRÖDINGER EQUATION

Yonglei Fang (), Xiong You () and Qinghe Ming ()
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Yonglei Fang: Department 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
Qinghe Ming: Department of Mathematics and Statistics, Zaozhuang University, Zaozhuang 277160, P. R. China

International Journal of Modern Physics C (IJMPC), 2013, vol. 24, issue 10, 1-9

Abstract: Two exponentially fitted two-derivative Runge–Kutta (EFTDRK) methods of algebraic order four are derived. The asymptotic expressions of the local errors for large energies are obtained. The numerical results in the integration of the radial Schrödinger equation with the Woods–Saxon potential show the high efficiency of our new methods compared to some famous optimized codes in the literature.

Keywords: Two-derivative Rung–Kutta method; exponential fitting; Schrödinger equation; error analysis; Woods–Saxon potential; 0.260; 95.10.E (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1142/S0129183113500733

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