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ADI-Euler and extrapolation methods for the two-dimensional fractional advection-dispersion equation. (English) Zbl 1146.76037
Summary: We consider a two-dimensional fractional advection-dispersion equation (2D-FADE) with variable coefficients in a finite domain. We use a new technique of combination of alternating directions implicit-Euler method (ADI-Euler), the unshifted Grünwald formula for the advection term, the right-shifted Grünwald formula for the diffusion term, and a Richardson extrapolation to establish an unconditionally stable second-order accurate difference method. Stability, consistency and convergence of the ADI-Euler method for 2D-FADE are examined. A numerical example with known exact solution is also presented, and the behavior of the error is analyzed to verify the order of convergence of the ADI-Euler method and the extrapolated ADI-Euler method.
MSC:
76M20Finite difference methods (fluid mechanics)
76R99Diffusion and convection (fluid mechanics)
65M12Stability and convergence of numerical methods (IVP of PDE)
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