Space-Time Spectral Collocation Algorithm for the Variable-Order Galilei Invariant Advection Diffusion Equations with a Nonlinear Source Term. Issue 1 (2nd January 2017)

• Record Type: Journal Article
• Authors: Abd-Elkawy, Mohamed A.; Alqahtani, Rubayyi T.
• Is Part Of: Mathematical modelling and analysis. Volume 22:Issue 1(2017)
• Page Start: 1
• Page End: 20
• Publication Date: 2017-01-02
• Subjects: variable-order Galilei invariant advection diffusion equation -- fractional calculus -- collocation method -- Gauss-Radau quadrature -- Gauss-Lobatto quadrature; 42C05 -- 65D99 -- 35R11 -- 65N35; Mathematical models -- Periodicals; Mathematical models -- Study and teaching -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis -- Problems, exercises, etc -- Periodicals; Mathematical analysis; Mathematical models; Mathematical models -- Study and teaching; Periodicals; Problems and exercises; 511.805
• DOI: 10.3846/13926292.2017.1258014
• Languages: English
• ISSNs: 1392-6292

Abstract

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.