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A characteristic difference method for the transient fractional convection-diffusion equations. (English) Zbl 1225.65085
The authors present a new characteristic finite difference method for solving the two-sided space-fractional convection-diffusion equation. The method is a combination of characteristic methods and fractional finite difference methods. They discuss the stability, consistency and convergence of the new method, and give numerical experiments to compare it with other known methods. The results in the paper show that the new method is especially efficient and superior for the high-dimensional convection-dominated diffusion equations.
MSC:
65M06Finite difference methods (IVP of PDE)
35K20Second order parabolic equations, initial boundary value problems
35R11Fractional partial differential equations
65M12Stability and convergence of numerical methods (IVP of PDE)
65M25Method of characteristics (IVP of PDE, numerical methods)
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