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An Explicit Hermite-Taylor Method for the Schrödinger Equation

Part of: Applications to specific physical systems Numerical analysis: Ordinary differential equations

Published online by Cambridge University Press:  27 March 2017

Daniel Appelö ,
Gunilla Kreiss  and
Siyang Wang
Daniel Appelö*
Affiliation:
Department of Mathematics and Statistics, University of New Mexico, 1 University of New Mexico, Albuquerque, NM 87131, USA
Gunilla Kreiss*
Affiliation:
Division of Scientific Computing, Department of Information Technology, Uppsala University, Box 337, 75105 Uppsala, Sweden
Siyang Wang*
Affiliation:
Division of Scientific Computing, Department of Information Technology, Uppsala University, Box 337, 75105 Uppsala, Sweden
*
*Corresponding author. Email addresses:appelo@math.unm.edu (D. Appelö), gunilla.kreiss@it.uu.se (G. Kreiss), siyang.wang@it.uu.se (S.Wang)
*Corresponding author. Email addresses:appelo@math.unm.edu (D. Appelö), gunilla.kreiss@it.uu.se (G. Kreiss), siyang.wang@it.uu.se (S.Wang)
*Corresponding author. Email addresses:appelo@math.unm.edu (D. Appelö), gunilla.kreiss@it.uu.se (G. Kreiss), siyang.wang@it.uu.se (S.Wang)
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Abstract

An explicit spectrally accurate order-adaptive Hermite-Taylor method for the Schrödinger equation is developed. Numerical experiments illustrating the properties of the method are presented. The method, which is able to use very coarse grids while still retaining high accuracy, compares favorably to an existing exponential integrator – high order summation-by-parts finite difference method.

Keywords

Hermite methodSchrödinger equationhigh order

MSC classification

Secondary: 65L20: Stability and convergence of numerical methods 81V10: Electromagnetic interaction; quantum electrodynamics
Type
Research Article
Information
Communications in Computational Physics , Volume 21 , Issue 5 , May 2017 , pp. 1207 - 1230
Copyright
Copyright © Global-Science Press 2017 

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Footnotes

Communicated by Chi-Wang Shu

References

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