Numerical investigation of the solutions of Schrödinger equation with exponential cubic B-spline finite element method

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International Journal of Nonlinear Sciences and Numerical Simulation, vol.22, pp.119-133, 2021 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 22
  • Publication Date: 2021
  • Doi Number: 10.1515/ijnsns-2016-0179
  • Journal Name: International Journal of Nonlinear Sciences and Numerical Simulation
  • Journal Indexes: Science Citation Index Expanded, Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.119-133
  • Keywords: exponential spline, Schrodinger equation, soliton


© 2020 Walter de Gruyter GmbH, Berlin/Boston 2020.In this paper, we investigate the numerical solutions of the cubic nonlinear Schrödinger equation via the exponential cubic B-spline collocation method. Crank-Nicolson formulas are used for time discretization of the target equation. A linearization technique is also employed for the numerical purpose. Four numerical examples related to single soliton, collision of two solitons that move in opposite directions, the birth of standing and mobile solitons and bound state solution are considered as the test problems. The accuracy and the efficiency of the purposed method are measured by max error norm and conserved constants. The obtained results are compared with the possible analytical values and those in some earlier studies.