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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:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
35R11 Fractional partial differential equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M25 Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs

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