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Finite difference methods for fractional differential equations. (English) Zbl 1258.34018
Summary: The finite difference methods (FDMs) for the fractional differential equations are displayed. The considered equations mainly include the fractional kinetic equations of diffusion or dispersion with time, space and time-space derivatives. In some way, these numerical methods have similar form as the case for classical equations, some of which can be seen as the generalizations of the FDMs for the typical differential equations. And the classical tools, such as the von Neumann analysis method, the energy method and the Fourier method are extended to numerical methods for fractional differential equations accordingly. At the same time, the techniques for improving the accuracy and reducing the computation and storage are also introduced.
MSC:
34A08Fractional differential equations
35R11Fractional partial differential equations
65L12Finite difference methods for ODE (numerical methods)
65M06Finite difference methods (IVP of PDE)