GALERKIN METHODS FOR THE NUMERICAL SOLUTION OF THE SCHRÖDINGER EQUATION BY USING TRIGONOMETRIC B-SPLINES

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Mersin M., IRK D., ZORŞAHİN GÖRGÜLÜ M.

Miskolc Mathematical Notes, cilt.23, sa.1, ss.363-380, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 23 Sayı: 1
  • Basım Tarihi: 2022
  • Doi Numarası: 10.18514/mmn.2022.3441
  • Dergi Adı: Miskolc Mathematical Notes
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
  • Sayfa Sayıları: ss.363-380
  • Anahtar Kelimeler: Schr?dinger equation, Galerkin finite element method, quadratic trigonometric B-spline function, cubic trigonometric B-spline function, quartic trigonometric B-spline function, quintic trigonometric B-spline function, FINITE-ELEMENT-METHOD
  • Eskişehir Osmangazi Üniversitesi Adresli: Evet

Özet

© 2022. Miskolc University PressThis paper includes four finite element methods which are based on quadratic, cubic, quartic and quintic trigonometric B-spline functions for space discretization and Crank-Nicolson method for time discretization, to be achieved the numerical solution of the Schrödinger equation (SE). The algorithms obtained by different degrees trigonometric B-spline Galerkin methods are new for getting numerical solution of the SE. To see the accuracy of the proposed methods, two numerical experiments are investigated and the comparison of the methods are given in the test problem section.