A parametric symmetric linear four-step method for the efficient integration of the Schrödinger equation and related oscillatory problems

@article{Anastassi2012APS,
  title={A parametric symmetric linear four-step method for the efficient integration of the Schr{\"o}dinger equation and related oscillatory problems},
  author={Zacharias A. Anastassi and Theodore E. Simos},
  journal={J. Computational Applied Mathematics},
  year={2012},
  volume={236},
  pages={3880-3889}
}
In this article, we develop an explicit symmetric linear phase-fitted four-step method with a free coefficient as parameter. The parameter is used for the optimization of the method in order to solve efficiently the Schrödinger equation and related oscillatory problems. We evaluate the local truncation error and the interval of periodicity as functions of the parameter. We reveal a direct relationship between the periodicity interval and the local truncation error. We also measure the… CONTINUE READING

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