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Zbl 1126.65121
Lin, Yumin; Xu, Chuanju
Finite difference/spectral approximations for the time-fractional diffusion equation. (English)
[J] J. Comput. Phys. 225, No. 2, 1533-1552 (2007). ISSN 0021-9991

Consider the problem of finding a numerical solution for the time-fractional diffusion equation with the fractional derivative with respect to time being given in the sense of Caputo. For the solution of this problem, the authors propose a method based on a finite difference scheme with respect to time combined with a Legendre spectral method for the space variable(s). A proof of stability and convergence of the algorithm is provided. Error estimates and numerical results are given as well.
[Kai Diethelm (Braunschweig)]

MSC 2000:: *65R20 Integral equations (numerical methods)
65M12 Stability and convergence of numerical methods (IVP of PDE)
65M06 Finite difference methods (IVP of PDE)
65M70 Spectral, collocation and related methods (IVP of PDE)
45K05 Integro-partial differential equations
26A33 Fractional derivatives and integrals (real functions)
35K15 Second order parabolic equations, initial value problems

Keywords: Caputo derivative; time-fractional diffusion equation; finite difference method; spectral method; stability; convergence; numerical results

Cited in: Zbl 1259.65151

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