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Stability and convergence of a new explicit finite-difference approximation for the variable-order nonlinear fractional diffusion equation

Lin, R., Liu, Fawang, Anh, Vo, & Turner, Ian W. (2009) Stability and convergence of a new explicit finite-difference approximation for the variable-order nonlinear fractional diffusion equation. Applied Mathematics and Computation, 212(2), pp. 435-445.

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Abstract

In this paper, we consider the variable-order nonlinear fractional diffusion equation

View the MathML source where xRα(x,t) is a generalized Riesz fractional derivative of variable order View the MathML source and the nonlinear reaction term f(u,x,t) satisfies the Lipschitz condition |f(u1,x,t)-f(u2,x,t)|less-than-or-equals, slantL|u1-u2|. A new explicit finite-difference approximation is introduced. The convergence and stability of this approximation are proved. Finally, some numerical examples are provided to show that this method is computationally efficient. The proposed method and techniques are applicable to other variable-order nonlinear fractional differential equations.

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42 citations in Web of Science®

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ID Code: 29758
Item Type: Journal Article
Keywords: Variable Order, Fractional Calculus, Nonlinear Fractional Diffusion Equation, Convergence, Stability, Explicit Difference Approximation
DOI: 10.1016/j.amc.2009.02.047
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
Copyright Owner: Copyright 2009 Elsevier
Deposited On: 19 Jan 2010 13:09
Last Modified: 01 Mar 2012 00:05

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