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International Journal of Nonlinear Sciences and Numerical Simulation

Editor-in-Chief: Birnir, Björn

Editorial Board: Armbruster, Dieter / Bessaih, Hakima / Chou, Tom / Grauer, Rainer / Marzocchella, Antonio / Rangarajan, Govindan / Trivisa, Konstantina / Weikard, Rudi

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Volume 19, Issue 3-4

Issues

Numerical Methods for the Derivative Nonlinear Schrödinger Equation

Shu-Cun Li / Xiang-Gui Li
  • Corresponding author
  • School of Applied Science,Beijing Information Science and Technology University,Beijing,100192 P.R. China
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/ Fang-Yuan Shi
Published Online: 2018-03-31 | DOI: https://doi.org/10.1515/ijnsns-2016-0184

Abstract

In this work, a second-order accuracy in both space and time Crank–Nicolson (C-N)-type scheme, a fourth-order accuracy in space and second-order accuracy in time compact scheme and a sixth-order accuracy in space and second-order accuracy in time compact scheme are proposed for the derivative nonlinear Schrödinger equation. The C-N-type scheme is tested to satisfy the conservation of discrete mass. For the two compact schemes, the iterative algorithm and the Thomas algorithm in block matrix form are adopted to enhance the computational efficiency. Numerical experiment is given to test the mass conservation for the C-N-type scheme as well as the accuracy order of the three schemes. In addition, the numerical simulation of binary collision and the influence on the solitary solution by adding a small random perturbation to the initial condition are also discussed.

Keywords: derivative nonlinear Schrödinger equation; compact methods; binary collision; random perturbation

MSC 2010: 65M06; 35L05; 81Q05; 81-08

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About the article

Published Online: 2018-03-31

Published in Print: 2018-06-26


This work is supported by National Natural Science Foundation of China (No. 11671044), the Science Challenge Project (No. TZ2016001) and Beijing Municipal Commission of Education (No. PXM2017\_014224\_000020).


Citation Information: International Journal of Nonlinear Sciences and Numerical Simulation, Volume 19, Issue 3-4, Pages 239–249, ISSN (Online) 2191-0294, ISSN (Print) 1565-1339, DOI: https://doi.org/10.1515/ijnsns-2016-0184.

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