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 (SJ...

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Published inMathematical modelling and analysis Vol. 22; no. 1; pp. 1 - 20
Main Authors Abd-Elkawy, Mohamed A., Alqahtani, Rubayyi T.
Format Journal Article
LanguageEnglish
Published Taylor & Francis 02.01.2017
Vilnius Gediminas Technical University
Subjects
Advection
Algorithms
Collocation
collocation method
Diffusion
Equations (Mathematics)
fractional calculus
Gauss-Lobatto quadrature
Gauss-Radau quadrature
Invariants
Invariants (Mathematics)
Mathematical analysis
Mathematical models
Mathematical research
Nonlinearity
Spectra
variable-order Galilei invariant advection diffusion equation
collocation method
fractional calculus
variable-order Galilei invariant advection diffusion equation
Gauss-Radau quadrature
Gauss-Lobatto quadrature
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Summary: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.
Bibliography:ObjectType-Article-1
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ISSN:1392-6292
1648-3510
DOI:10.3846/13926292.2017.1258014