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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.
MSC:
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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