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

    Authors

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

    Comments

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    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

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