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A new Jacobi spectral collocation method for solving 1+1 fractional Schrödinger equations and fractional coupled Schrödinger systems

  • A. H. Bhrawy
  • E. H. Doha
  • S. S. Ezz-Eldien
  • Robert A. Van Gorder
Regular Article

Abstract.

The Jacobi spectral collocation method (JSCM) is constructed and used in combination with the operational matrix of fractional derivatives (described in the Caputo sense) for the numerical solution of the time-fractional Schrödinger equation (T-FSE) and the space-fractional Schrödinger equation (S-FSE). The main characteristic behind this approach is that it reduces such problems to those of solving a system of algebraic equations, which greatly simplifies the solution process. In addition, the presented approach is also applied to solve the time-fractional coupled Schrödinger system (T-FCSS). In order to demonstrate the validity and accuracy of the numerical scheme proposed, several numerical examples with their approximate solutions are presented with comparisons between our numerical results and those obtained by other methods.

Keywords

Imaginary Part Fractional Derivative Collocation Method Fractional Calculus Operational Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • A. H. Bhrawy
    • 1
    • 2
  • E. H. Doha
    • 3
  • S. S. Ezz-Eldien
    • 4
  • Robert A. Van Gorder
    • 5
  1. 1.Department of Mathematics, Faculty of ScienceKing Abdulaziz UniversityJeddahSaudi Arabia
  2. 2.Department of Mathematics, Faculty of ScienceBeni-Suef UniversityBeni-SuefEgypt
  3. 3.Department of Mathematics, Faculty of ScienceCairo UniversityGizaEgypt
  4. 4.Department of Basic Science, Institute of Information TechnologyModern AcademyCairoEgypt
  5. 5.Department of MathematicsUniversity of Central FloridaOrlandoUSA

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