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Exponentially fitted TDRK pairs for the Schrödinger equation

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Abstract

Two exponentially fitted two-derivative Runge–Kutta pairs for the numerical integration of the Schrödinger equation are presented in this paper. The asymptotic expressions of the local errors for large energies are given. The numerical results in the integration of the radial Schrödinger equation with the Woods–Saxon potential and the Lennard-Jones potential show the high efficiency of our new methods when compared with some famous optimized codes in the literature.

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Acknowledgments

The authors are deeply grateful to the anonymous referees, for their valuable comments and suggestions. This research is partially supported by NSFC (No. 11101357) and the foundation of Scientific Research Project of Shandong Universities (No. J14LI04).

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  1. School of Mathematics and Statistics, Zaozhuang University, Zaozhuang, 277160, People’s Republic of China

    Yanping Yang, Ke Wu & Yonglei Fang

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  1. Yanping Yang
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Correspondence to Yonglei Fang.

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Yang, Y., Wu, K. & Fang, Y. Exponentially fitted TDRK pairs for the Schrödinger equation. J Math Chem 53, 1470–1487 (2015). https://doi.org/10.1007/s10910-015-0500-z

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