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A new modified embedded 5(4) pair of explicit Runge–Kutta methods for the numerical solution of the Schrödinger equation

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Abstract

In this work a new modified embedded 5(4) pair of explicit Runge–Kutta methods is developed for the numerical solution of the Schrödinger equation. We investigate the error of the new pair, based on the error analysis we apply the higher order method to the resonance problem, also we apply the new embedded pair to elastic scattering phase-shift problem. The applications show the efficiency of our new developed embedded pair and the higher order method.

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Acknowledgments

The authors are deeply grateful to the anonymous referees for their valuable comments and suggestions. This research was partially supported by NSFC (No. 11101357), the foundation of Shangdong Outstanding Young Scientists Award Project (No. BS2010SF031), NSF of Shandong Province (No. ZR2011AL006) and the foundation of Scientific Research Project of Shangdong Universities (No. J11LG69).

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

    Shiwei Liu, Juan Zheng & Yonglei Fang

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  1. Shiwei Liu
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  2. Juan Zheng
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  3. Yonglei Fang
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Correspondence to Shiwei Liu.

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Liu, S., Zheng, J. & Fang, Y. A new modified embedded 5(4) pair of explicit Runge–Kutta methods for the numerical solution of the Schrödinger equation. J Math Chem 51, 937–953 (2013). https://doi.org/10.1007/s10910-012-0127-2

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