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Quasi-wavelet method for time-dependent fractional partial differential equation. (English) Zbl 1284.65194

The authors present a numerical method for a time-fractional diffusion equation in one space dimension where the order of the time derivative is \(1/2\). The boundary conditions are homogeneous; the initial condition may be inhomogeneous. The equation is given in a slightly non-standard integro-differential form. This is handled by a time discretization that essentially amounts to a finite difference method. After an analysis of stability and convergence properties of the resulting semidiscrete equation, the space variable is discretized via a quasi-wavelet approach based on sinc functions. Some numerical results are given.

MSC:

65R20 Numerical methods for integral equations
45K05 Integro-partial differential equations
26A33 Fractional derivatives and integrals
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