# THDRK methods with vanished phase-lag and its first derivative for the Schrödinger equation

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## Abstract

Two new optimized three-derivative Runge–Kutta type methods with vanishing phase-lag and its first derivative for the numerical integration of Schrödinger equation are derived in this paper. We present the error analysis in terms of the asymptotic expressions of the local errors. Numerical results are reported to show the efficiency and robustness of the new methods for the numerical integration of the Schrödinger equation with the Woods–Saxon potential.

## Keywords

Three-derivative Runge–Kutta methods Phase-lag error Schrödinger equation Error analysis## Notes

### Acknowledgements

The authors are grateful to the anonymous referees for their careful review and for your invaluable suggestions which helped very much to improve the quality of the manuscript. This research was partially supported by the National Natural Science Foundation of China (No. 11571302),the project of Shandong Province higher Educational Science and Technology Program (Nos. KJ2018BAI031, J17KA190), the NSF of Shandong Province (No. ZR2018MA024) and the Jiangsu Provincial Natural Science Foundation (No. BK20171370).

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