An effective approach to numerical soliton solutions for the Schrodinger equation via modified cubic B-spline differential quadrature method

BAŞHAN A., YAĞMURLU N. M., UÇAR Y., ESEN A.

CHAOS SOLITONS & FRACTALS, cilt.100, ss.45-56, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 100
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1016/j.chaos.2017.04.038
  • Dergi Adı: CHAOS SOLITONS & FRACTALS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.45-56
  • Anahtar Kelimeler: Partial differential equations, Differential quadrature method, Strong stability-preserving Runge Kutta, Modified Cubic B-splines, Schrodinger equation, FINITE-ELEMENT, WAVES
  • İnönü Üniversitesi Adresli: Evet

Özet

In this study, an effective differential quadrature method (DQM) which is based on modified cubic B-spline (MCB) has been implemented to obtain the numerical solutions for the nonlinear Schrodinger (NLS) equation. After separating the Schrodinger equation into coupled real value differential equations,we have discretized using DQM and then obtained ordinary differential equation systems. For time integration, low storage strong stability-preserving Runge-Kutta method has been used. Numerical solutions of five different test problems have been obtained. The efficiency and accuracy of the method have been measured by calculating error norms L2 and Linfinity and two lowest invariants I1 and I2. Also relative changes of invariants are given. The newly obtained numerical results have been compared with the published numerical results and a comparison has shown that the MCB-DQM is an effective numerical scheme to solve the nonlinear Schrodinger equation. (C) 2017 Elsevier Ltd. All rights reserved.