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New numerical methods for the coupled nonlinear Schrödinger equations

New numerical methods for the coupled nonlinear Schrödinger equations In this paper, three numerical schemes with high accuracy for the coupled Schrödinger equations are studied. The conservative properties of the schemes are obtained and the plane wave solution is analysised. The split step Runge-Kutta scheme is conditionally stable by linearized analyzed. The split step compact scheme and the split step spectral method are unconditionally stable. The trunction error of the schemes are discussed. The fusion of two solitions colliding with different β is shown in the figures. The numerical experments demonstrate that our algorithms are effective and reliable. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

New numerical methods for the coupled nonlinear Schrödinger equations

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Publisher
Springer Journals
Copyright
Copyright © 2010 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Theoretical, Mathematical and Computational Physics; Math Applications in Computer Science; Applications of Mathematics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-007-7098-2
Publisher site
See Article on Publisher Site

Abstract

In this paper, three numerical schemes with high accuracy for the coupled Schrödinger equations are studied. The conservative properties of the schemes are obtained and the plane wave solution is analysised. The split step Runge-Kutta scheme is conditionally stable by linearized analyzed. The split step compact scheme and the split step spectral method are unconditionally stable. The trunction error of the schemes are discussed. The fusion of two solitions colliding with different β is shown in the figures. The numerical experments demonstrate that our algorithms are effective and reliable.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Mar 18, 2010

References