Finite difference/spectral approximations for the time-fractional diffusion equation
作者： Yumin Lin , Chuanju Xu
DOI: 10.1016/J.JCP.2007.02.001
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摘要: In this paper, we consider the numerical resolution of a time-fractional diffusion equation, which is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative (of order α, with 0⩽ α⩽ 1). The main purpose of this work is to construct and analyze stable and high order scheme to efficiently solve the time-fractional diffusion equation. The proposed method is based on a finite difference scheme in time and Legendre spectral methods in space. Stability and convergence of the method are …
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Rudolf Gorenflo, Francesco Mainardi, Daniele Moretti, Paolo Paradisi, Time Fractional Diffusion: A Discrete Random Walk Approach Nonlinear Dynamics. ,vol. 29, pp. 129- 143 ,(2002) , 10.1023/A:1016547232119
Om P. Agrawal, Solution for a Fractional Diffusion-Wave Equation Defined in a Bounded Domain Nonlinear Dynamics. ,vol. 29, pp. 145- 155 ,(2002) , 10.1023/A:1016539022492
F. Liu, S. Shen, V. Anh, I. Turner, Analysis of a discrete non-Markovian random walk approximation for the time fractional diffusion equation Anziam Journal. ,vol. 46, pp. 488- 504 ,(2005) , 10.21914/ANZIAMJ.V46I0.973
Kai Diethelm, Alan D. Freed, On the Solution of Nonlinear Fractional-Order Differential Equations Used in the Modeling of Viscoplasticity Springer, Berlin, Heidelberg. pp. 217- 224 ,(1999) , 10.1007/978-3-642-60185-9_24
Alberto Carpinteri, Francesco Mainardi, Fractals and fractional calculus in continuum mechanics Springer-Verlag. ,(1997) , 10.1007/978-3-7091-2664-6
Kai Diethelm, Neville J. Ford, NUMERICAL SOLUTION OF THE BAGLEY-TORVIK EQUATION ∗ Bit Numerical Mathematics. ,vol. 42, pp. 490- 507 ,(2002) , 10.1023/A:1021973025166
Alfio Quarteroni, Alberto Valli, Numerical Approximation of Partial Differential Equations Springer Series in Computational Mathematics. ,vol. 23, pp. 1- 544 ,(1994) , 10.1007/978-3-540-85268-1
W. R. Schneider, W. Wyss, Fractional diffusion and wave equations Journal of Mathematical Physics. ,vol. 30, pp. 134- 144 ,(1989) , 10.1063/1.528578
G.J. Fix, J.P. Roof, Least squares finite-element solution of a fractional order two-point boundary value problem Computers & Mathematics With Applications. ,vol. 48, pp. 1017- 1033 ,(2004) , 10.1016/J.CAMWA.2004.10.003
V.E. Lynch, B.A. Carreras, D. del-Castillo-Negrete, K.M. Ferreira-Mejias, H.R. Hicks, Numerical methods for the solution of partial differential equations of fractional order Journal of Computational Physics. ,vol. 192, pp. 406- 421 ,(2003) , 10.1016/J.JCP.2003.07.008