NUMERICAL SPECTRAL LEGENDRE APPROACH FOR SOLVING SPACE-TIME FRACTIONAL ADVECTION-DISPERSION PROBLEMS | Zendy

E. H. Doha | Zendy; W. M. AbdElhameed | Zendy; Nermeen A Elkot | Zendy; Y. H. Youssri | Zendy

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NUMERICAL SPECTRAL LEGENDRE APPROACH FOR SOLVING SPACE-TIME FRACTIONAL ADVECTION-DISPERSION PROBLEMS

Author(s) -

E. H. Doha,

W. M. AbdElhameed,

Nermeen A Elkot,

Y. H. Youssri

Publication year - 2018

Publication title -

journal of the egyptian mathematical society

Language(s) - English

Resource type - Journals

eISSN - 2090-9128

pISSN - 1110-256X

DOI - 10.21608/jomes.2018.9472

Subject(s) - mathematics , legendre polynomials , algebraic equation , advection , spectral method , algebraic number , robustness (evolution) , numerical analysis , dispersion (optics) , mathematical analysis , mathematical optimization , nonlinear system , physics , biochemistry , chemistry , quantum mechanics , gene , optics , thermodynamics

This manuscript is devoted to implementing spectral numerical solutions to two kinds of fractional space-time advectiondispersion problems governed by certain constraints conditions. The collocation and tau spectral methods are utilized for obtaining the proposed spectral solutions. A double Legendre expansion is proposed as an approximate solution. The main idea of the algorithm is basically depend on converting the equation with its constraints conditions into linear or nonlinear systems of algebraic equations which can be efficiently solved with the aid of suitable numerical solvers. Some illustrative examples are displayed aiming to confirm robustness, efficiency and accuracy of the proposed spectral solutions.

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