Title

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

Authors

Authors

A. H. Bhrawy; E. H. Doha; S. S. Ezz-Eldien;R. A. Van Gorder

Comments

Authors: contact us about adding a copy of your work at STARS@ucf.edu

Abbreviated Journal Title

Eur. Phys. J. Plus

Keywords

PARTIAL-DIFFERENTIAL-EQUATIONS; DISCONTINUOUS GALERKIN METHOD; QUANTUM-MECHANICS; INTEGRODIFFERENTIAL EQUATIONS; VARIABLE-COEFFICIENTS; DIFFUSION-EQUATIONS; OPERATIONAL MATRIX; NUMERICAL-SOLUTION; TAU METHOD; ORDER; Physics, Multidisciplinary

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 Schrodinger equation (T-FSE) and the space-fractional Schrodinger 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 Schrodinger 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.

Journal Title

European Physical Journal Plus

Volume

129

Issue/Number

12

Publication Date

1-1-2014

Document Type

Article

Language

English

First Page

21

WOS Identifier

WOS:000346187800001

ISSN

2190-5444

Share

COinS