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Journal of Mathematical Chemistry

, Volume 57, Issue 5, pp 1413–1426 | Cite as

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

  • Shiwei Liu
  • Juan Zheng
  • Yonglei FangEmail author
Original Paper
  • 126 Downloads

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.

Keywords

Embedded TDRK pair Lennard-Jones potential Schrödinger equation 

Notes

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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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsZaozhuang UniversityZaozhuangPeople’s Republic of China

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