Approximate solution of the fractional advection-dispersion equation. (English) Zbl 1210.65168

The solution of the advection-dispersion equation of fractional order
\[ \frac{\partial^{\alpha}u(x,t)}{\partial t^{\alpha}}+ v(x,t)D_{x}^{\nu}u(x,t)-k(x,t)D_{x}^{\beta}u(x,t)=F(x,t) \]
with homogeneous initial and boundary conditions is presented in the form of Fourier series. The approximate solution is obtained by truncating this series.


65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
35L50 Initial-boundary value problems for first-order hyperbolic systems
35R11 Fractional partial differential equations
35C10 Series solutions to PDEs
46E22 Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)
Full Text: DOI


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