Finite difference schemes for time-fractional Schrodinger equations via fractional linear multistep method


HİÇDURMAZ B.

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2020 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume:
  • Publication Date: 2020
  • Doi Number: 10.1080/00207160.2020.1834088
  • Journal Name: INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded, Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, Computer & Applied Sciences, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: Fractional linear multistep method, time-fractional Schr&#246, dinger equation, stability, fractional derivative, convergence, NUMERICAL-METHOD, SUBDIFFUSION, EXISTENCE, COLLOCATION, ALGORITHMS

Abstract

In this paper, a finite difference-based numerical approach is developed for time-fractional Schrodinger equations with one or multidimensional space variables, with the use of fractional linear multistep method for time discretization and finite difference method for spatial discretization. The proposed method leads to achieve second order of accuracy for time variable. Stability and convergence theorems for the constructed difference scheme is achieved via z-transform method. Time-fractional Schrodinger equation is considered in abstract form to allow generalization of the theoretical results on problems which have distinct spatial operators with or without variable coefficients. Numerical results are presented on one and multidimensional experimental problems to verify the theoretical results.