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Numerical simulation for the variable-order Galilei invariant advection diffusion equation with a nonlinear source term

Chen, Chang-Ming, Liu, Fawang, Anh, Vo, & Turner, Ian (2011) Numerical simulation for the variable-order Galilei invariant advection diffusion equation with a nonlinear source term. Applied Mathematics and Computation, 217(12), pp. 5729-5742.

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Abstract

In this paper, we consider the variable-order Galilei advection diffusion equation with a nonlinear source term. A numerical scheme with first order temporal accuracy and second order spatial accuracy is developed to simulate the equation. The stability and convergence of the numerical scheme are analyzed. Besides, another numerical scheme for improving temporal accuracy is also developed. Finally, some numerical examples are given and the results demonstrate the effectiveness of theoretical analysis.

Keywords: The variable-order Galilei invariant advection diffusion equation with a nonlinear source term; The variable-order Riemann–Liouville fractional partial derivative; Stability; Convergence; Numerical scheme improving temporal accuracy

Impact and interest:

6 citations in Scopus
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4 citations in Web of Science®

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56 since deposited on 13 Jul 2011
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ID Code: 42692
Item Type: Journal Article
Keywords: The variable-order Galilei invariant advection diffusion equation with a nonlinear source term, The variable-order Riemann-Liouville fractional partial derivative, Stability, Convergence, Numerical scheme improving temporal accuracy
DOI: 10.1016/j.amc.2010.12.049
ISSN: 0096-3003
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200)
Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300)
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Past > Schools > Mathematical Sciences
Deposited On: 13 Jul 2011 23:06
Last Modified: 08 Dec 2012 18:05

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