The meshless kernel-based method of lines for the numerical solution of the nonlinear Schrodinger equation

Dereli Y.

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, vol.36, no.9, pp.1416-1423, 2012 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 36 Issue: 9
  • Publication Date: 2012
  • Doi Number: 10.1016/j.enganabound.2012.02.018
  • Journal Name: ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1416-1423
  • Keywords: NLS equation, Kernel based, Method of lines, Radial basis functions, DIFFERENTIAL QUADRATURE ALGORITHM, ORTHOGONAL SPLINE COLLOCATION, DISCRETIZATION METHOD QDM, FINITE-ELEMENT-METHOD, SOLITON, WAVES, MEDIA
  • Anadolu University Affiliated: Yes

Abstract

In this paper, the nonlinear Schrodinger equation is solved numerically by using the meshless kernel-based method of lines. Multiquadric, Gaussian and Wend land's compactly supported radial basis functions are used as the kernel basis functions. In the numerical examples, the single soliton solution, interaction of two colliding solitons, birth of standing soliton, birth of mobile soliton and bound state of solitons are simulated. The accuracy and efficiency of the used method are tested by computing the lowest two invariants and the relative change of invariants for all test problems. Error norms L-2 and L-infinity are computed for single soliton motion whose exact solution is known. Numerical results and figures off wave motions for all test problems are presented. The numerical solutions of the nonlinear Scrodinger equation are compared with both the analytical solutions and numerical solutions of some earlier papers in the literature. (C) 2012 Elsevier Ltd. All rights reserved.