Abstract
In this paper, we consider the numerical solution of the space fractional diffusion equation, which is obtained from the standard diffusion equation by replacing the second-order space derivative with a fractional derivative (of order α, with 1<;α≤2). The main purpose of this work is to construct scheme to efficiently solve the space fractional diffusion equation. We get a forward Euler scheme with finite difference method. We attain a weak formulation of finite element method from the above scheme. Convergence of the method is rigorously established. Numerical experiments are carried out to support the theoretical predictions.
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