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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 α, with 1<α2. 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.
MSC:
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)
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