# 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} }

- Published 2012 in J. Computational Applied Mathematics
DOI:10.1016/j.cam.2012.03.016

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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#### References

##### Publications referenced by this paper.

Showing 1-10 of 46 references

## Two new optimized eight-step symmetric methods for the efficient solution of the Schrödinger Equation and related problems

View 1 Excerpt

## An optimized explicit Runge–Kutta method with increased phase-lag order for the numerical solution of the Schrödinger equation and related problems

View 1 Excerpt

## Exponentially and trigonometrically fitted methods for the solution of the schrodinger equation

View 1 Excerpt

## High algebraic order methods with vanished phase-lag and its first derivative for the numerical solution of the Schrödinger equation

View 1 Excerpt

## Multistepmethods with vanished phase-lag and its first and second derivatives for the numerical integration of the Schrödinger equation

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## Numerical multistep methods for the efficient solution of quantum mechanics and related problems

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