Taylor collocation method for the numerical solution of the nonlinear Schrodinger equation using quintic B-spline basis

Aksoy A. M., Irk D., Dag İ.

PHYSICS OF WAVE PHENOMENA, vol.20, no.1, pp.67-79, 2012 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 20 Issue: 1
  • Publication Date: 2012
  • Doi Number: 10.3103/s1541308x12010086
  • Journal Name: PHYSICS OF WAVE PHENOMENA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.67-79
  • Eskisehir Osmangazi University Affiliated: Yes

Abstract

In this study, we construct a Taylor collocation method for the numerical solution of the nonlinear Schrodinger (NLS) equation. We use suitable initial and boundary conditions. Taylor series expansion is used for time discretization. The cubic B-spline collocation method is applied to spatial discretization. Test problems concerning the single soliton motion, interaction of two colliding solitons, and the formation and bound states of solitons of the NLS equation are studied to evaluate the method. The L (2) and L (a) error norms are calculated to improve the accuracy of the numerical results.