Stability and convergence of a new explicit finite-difference approximation for the variable-order nonlinear fractional diffusion equation
Data(s) |
2009
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Resumo |
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. |
Formato |
application/pdf |
Identificador | |
Publicador |
Elsevier |
Relação |
http://eprints.qut.edu.au/29758/1/29758.pdf DOI:10.1016/j.amc.2009.02.047 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. |
Direitos |
Copyright 2009 Elsevier |
Fonte |
Faculty of Science and Technology; Mathematical Sciences |
Palavras-Chave | #010200 APPLIED MATHEMATICS #010300 NUMERICAL AND COMPUTATIONAL MATHEMATICS #Variable Order #Fractional Calculus #Nonlinear Fractional Diffusion Equation #Convergence #Stability #Explicit Difference Approximation |
Tipo |
Journal Article |