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A new embedded 4(3) pair of modified two-derivative Runge–Kutta methods with FSAL property for the numerical solution of the Schrödinger equation

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Abstract

A new embedded 4(3) pair of modified two-derivative Runge–Kutta (TDRK) methods with First Same As Last (FSAL) property for the numerical solution of the Schrödinger equation is constructed in this paper. Both the error analysis and phase properties indicate good accuracy of the new pair especially for large eigenvalues. An application to the well-known Lennard-Jones potential confirms the theory and shows that the new pair is more efficient than some high-quality Runge–Kutta(–Nyström) pairs in the literature.

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Acknowledgements

This work was partially supported by the Natural Science Foundation of China (NSFC) (No. 11571302), the Natural Science Foundation of Shandong Province, China (No. ZR2018MA024) and the Project of Shandong Province Higher Educational Science and Technology Program (No. KJ2018BAI031, No. J17KA190).

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Correspondence to Yonglei Fang.

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Liu, S., Zheng, J. & Fang, Y. A new embedded 4(3) pair of modified two-derivative Runge–Kutta methods with FSAL property for the numerical solution of the Schrödinger equation. J Math Chem 57, 1413–1426 (2019). https://doi.org/10.1007/s10910-018-0974-6

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Keywords

  • Embedded TDRK pair
  • Lennard-Jones potential
  • Schrödinger equation