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An Explicit Hermite-Taylor Method for the Schrödinger Equation

Published online by Cambridge University Press:  27 March 2017

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.

Type
Research Article
Copyright
Copyright © Global-Science Press 2017 

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Footnotes

Communicated by Chi-Wang Shu

References

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