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

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 (S...

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Main Authors:	Mohamed A. Abd-Elkawy, Rubayyi T. Alqahtani
Format:	Article
Language:	English
Published:	Vilnius Gediminas Technical University 2017-01-01
Series:	Mathematical Modelling and Analysis
Subjects:	variable-order Galilei invariant advection diffusion equation fractional calculus collocation method Gauss-Radau quadrature Gauss-Lobatto quadrature
Online Access:	https://journals.vgtu.lt/index.php/MMA/article/view/869

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record_format	Article
spelling	doaj-3d887d85adc54f17a2523dc00edfa1bd2021-07-02T12:06:20ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102017-01-0122110.3846/13926292.2017.1258014Space-Time Spectral Collocation Algorithm for the Variable-Order Galilei Invariant Advection Diffusion Equations with a Nonlinear Source TermMohamed A. Abd-Elkawy0Rubayyi T. Alqahtani1Department of Mathematics and Statistics, College of Science, Al-Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia; Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, EgyptDepartment of Mathematics and Statistics, College of Science, Al-Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia 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. https://journals.vgtu.lt/index.php/MMA/article/view/869variable-order Galilei invariant advection diffusion equationfractional calculuscollocation methodGauss-Radau quadratureGauss-Lobatto quadrature
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Mohamed A. Abd-Elkawy Rubayyi T. Alqahtani
spellingShingle	Mohamed A. Abd-Elkawy Rubayyi T. Alqahtani Space-Time Spectral Collocation Algorithm for the Variable-Order Galilei Invariant Advection Diffusion Equations with a Nonlinear Source Term Mathematical Modelling and Analysis variable-order Galilei invariant advection diffusion equation fractional calculus collocation method Gauss-Radau quadrature Gauss-Lobatto quadrature
author_facet	Mohamed A. Abd-Elkawy Rubayyi T. Alqahtani
author_sort	Mohamed A. Abd-Elkawy
title	Space-Time Spectral Collocation Algorithm for the Variable-Order Galilei Invariant Advection Diffusion Equations with a Nonlinear Source Term
title_short	Space-Time Spectral Collocation Algorithm for the Variable-Order Galilei Invariant Advection Diffusion Equations with a Nonlinear Source Term
title_full	Space-Time Spectral Collocation Algorithm for the Variable-Order Galilei Invariant Advection Diffusion Equations with a Nonlinear Source Term
title_fullStr	Space-Time Spectral Collocation Algorithm for the Variable-Order Galilei Invariant Advection Diffusion Equations with a Nonlinear Source Term
title_full_unstemmed	Space-Time Spectral Collocation Algorithm for the Variable-Order Galilei Invariant Advection Diffusion Equations with a Nonlinear Source Term
title_sort	space-time spectral collocation algorithm for the variable-order galilei invariant advection diffusion equations with a nonlinear source term
publisher	Vilnius Gediminas Technical University
series	Mathematical Modelling and Analysis
issn	1392-6292 1648-3510
publishDate	2017-01-01
description	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.
topic	variable-order Galilei invariant advection diffusion equation fractional calculus collocation method Gauss-Radau quadrature Gauss-Lobatto quadrature
url	https://journals.vgtu.lt/index.php/MMA/article/view/869
work_keys_str_mv	AT mohamedaabdelkawy spacetimespectralcollocationalgorithmforthevariableordergalileiinvariantadvectiondiffusionequationswithanonlinearsourceterm AT rubayyitalqahtani spacetimespectralcollocationalgorithmforthevariableordergalileiinvariantadvectiondiffusionequationswithanonlinearsourceterm
_version_	1721330375684259840

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

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