Title: Numerical approximation for the fractional diffusion equation via splines
Abstract: 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 < α ≤ 2. We consider the Caputo derivative as the space derivative, which is a form of representing the fractional derivative by an integral operator. The numerical solution is derived using Crank-Nicolson method in time combined with a spline approximation for the Caputo derivative in space. Consistency and convergence of the method is examined and numerical results are presented.
Publication Year: 2009
Publication Date: 2009-01-01
Language: en
Type: article
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Cited By Count: 2
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