Implicit difference approximation of the Galilei invariant fractional advection diffusion equation

Changming Chen, Fawang Liu, Ian Turner, Vo Anh


A Galilei invariant fractional advection diffusion equation with initial-boundary conditions is considered. An implicit difference approximation for solving the Galilei invariant fractional advection diffusion equation is presented. We introduce a new Fourier method for analyzing the stability and convergence of the implicit difference approximation. Finally, some numerical examples are given. The numerical results are in good agreement with our theoretical analysis. This method and supporting theoretical techniques can also be extended to a larger class of fractional integro-differential equations.

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