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Zbl 1179.65107
Cui, Mingrong
Compact finite difference method for the fractional diffusion equation. (English)
[J] J. Comput. Phys. 228, No. 20, 7792-7804 (2009). ISSN 0021-9991

The author apply for solving the one-dimensional fractional diffusion equation $$\frac{\partial u}{\partial t}=_{0}D^{1-\gamma} _{t} [K_{\gamma}\frac{\partial^{2}u}{\partial x^{2}}]+f(x,t),\quad x\in(L_{0},L_{1}), \quad t\in (0,T) $$ a special finite difference method using the Grunwald discretization process for the fractional derivative. The approximate scheme has an error of fourth order for the spatial variable and of first order for the time variable. The stability of this scheme is proved using Fourier series to expand the error of the approximate system.
[Ivan Secrieru (Chişinău)]

MSC 2000:: *65M06 Finite difference methods (IVP of PDE)
65M12 Stability and convergence of numerical methods (IVP of PDE)
35R11
35K05 Heat equation
65M15 Error bounds (IVP of PDE)

Keywords: fractional diffusion equation; finite difference method; stability; convergence; error bound; compact scheme; Padé approximant; Grunwald discretization

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Zentralblatt MATH Berlin [Germany]