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Numerical approximations for fractional diffusion equations via splines. (English) Zbl 1228.65153
Summary: A one-dimensional fractional diffusion model is considered, where the usual second order derivative gives place to a fractional derivative of order $\alpha $, with $1<\alpha \le 2$. We consider the Caputo derivative as the space derivative, which is a form of representing the fractional derivative by an integral operator. An implicit numerical method is derived which uses a spline approximation for the Caputo derivative. The consistency and stability of the method are examined and numerical results are presented.

65M06Finite difference methods (IVP of PDE)
35R11Fractional partial differential equations
26A33Fractional derivatives and integrals (real functions)
45K05Integro-partial differential equations
65M12Stability and convergence of numerical methods (IVP of PDE)
Full Text: DOI
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