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Space-Time Spectral Collocation Algorithm for the Variable-Order Galilei Invariant Advection Diffusion Equations with a Nonlinear Source Term

    Mohamed A. Abd-Elkawy Affiliation
    ; Rubayyi T. Alqahtani Affiliation

Abstract

This paper presents a space-time spectral collocation technique for solving the variable-order Galilei invariant advection diffusion equation with a nonlinear source term (VO-NGIADE). We develop a collocation scheme to approximate VONGIADE by means of the shifted Jacobi-Gauss-Lobatto collocation (SJ-GL-C) and shifted Jacobi-Gauss-Radau collocation (SJ-GR-C) methods. We successfully extend the proposed technique to solve the two-dimensional space VO-NGIADE. The discussed numerical tests illustrate the capability and high accuracy of the proposed methodologies.

Keyword : variable-order Galilei invariant advection diffusion equation, fractional calculus, collocation method, Gauss-Radau quadrature, Gauss-Lobatto quadrature

How to Cite
Abd-Elkawy, M. A., & Alqahtani, R. T. (2017). Space-Time Spectral Collocation Algorithm for the Variable-Order Galilei Invariant Advection Diffusion Equations with a Nonlinear Source Term. Mathematical Modelling and Analysis, 22(1), 1-20. https://doi.org/10.3846/13926292.2017.1258014
Published in Issue
Jan 11, 2017
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This work is licensed under a Creative Commons Attribution 4.0 International License.