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Spectral regularization method for a Cauchy problem of the time fractional advection-dispersion equation. (English) Zbl 1186.65128
Authors’ abstract: A Cauchy problem for the time fractional advection-dispersion equation (TFADE) is investigated. Such a problem is obtained from the classical advection-dispersion equation by replacing the first-order time derivative by the Caputo fractional derivative of order α(0<α1). We show that the Cauchy problem of TFADE is severely ill-posed and further apply a spectral regularization method to solve it based on the solution given by the Fourier method. The convergence estimate is obtained under a priori bound assumptions for the exact solution. Numerical examples are given to show the effectiveness of the proposed numerical method.
MSC:
65M30Improperly posed problems (IVP of PDE, numerical methods)
35R11Fractional partial differential equations
35R25Improperly posed problems for PDE
65M12Stability and convergence of numerical methods (IVP of PDE)
65M70Spectral, collocation and related methods (IVP of PDE)
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