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

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ERSOY HEPSON Ö., DAĞ İ.

International Journal of Nonlinear Sciences and Numerical Simulation, cilt.22, ss.119-133, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 22
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1515/ijnsns-2016-0179
  • Dergi Adı: International Journal of Nonlinear Sciences and Numerical Simulation
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.119-133
  • Anahtar Kelimeler: exponential spline, Schrodinger equation, soliton
  • Eskişehir Osmangazi Üniversitesi Adresli: Evet

Özet

© 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.