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Finite difference/spectral approximations for the time-fractional diffusion equation. (English) Zbl 1126.65121
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.

65R20Integral equations (numerical methods)
65M12Stability and convergence of numerical methods (IVP of PDE)
65M06Finite difference methods (IVP of PDE)
65M70Spectral, collocation and related methods (IVP of PDE)
45K05Integro-partial differential equations
26A33Fractional derivatives and integrals (real functions)
35K15Second order parabolic equations, initial value problems
Full Text: DOI
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