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

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...

Full description

Bibliographic Details
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
Description
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.
ISSN:1392-6292
1648-3510

Similar Items