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

Mathematical Modelling and Analysis

卷:22

Rubayyi T. Alqahtani¹  Mohamed A. Abd-Elkawy² 

[1] Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt;

[2] Department of Mathematics and Statistics, College of Science, Al-Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia;

关键词: variable-order Galilei invariant advection diffusion equation;    fractional calculus;    collocation method;    Gauss-Radau quadrature;    Gauss-Lobatto quadrature;   

DOI  :  10.3846/13926292.2017.1258014

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown