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A numerical approximation method for solving a three-dimensional space Galilei invariant fractional advection-diffusion equation. (English) Zbl 1177.26009
Summary: A numerical approximation method for solving a three-dimensional space Galilei invariant fractional advection diffusion equation is presented. The convergence and stability of the numerical approximation method are discussed by a new technique of Fourier analysis. The solvability of the numerical approximation method also is analyzed. Finally, applying Richardson extrapolation technique, a high-accuracy algorithm is structured and the numerical example demonstrated the theoretical results.
26A33Fractional derivatives and integrals (real functions)
65M12Stability and convergence of numerical methods (IVP of PDE)
65M06Finite difference methods (IVP of PDE)
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