A Space-Time Spectral Method for the Time Fractional Diffusion Equation

@article{Li2009ASS,
  title={A Space-Time Spectral Method for the Time Fractional Diffusion Equation},
  author={Xianjuan Li and Chuanju Xu},
  journal={SIAM J. Numerical Analysis},
  year={2009},
  volume={47},
  pages={2108-2131}
}
In this paper, we consider the numerical solution of the time fractional diffusion equation. Essentially, the time fractional diffusion equation differs from the standard diffusion equation in the time derivative term. In the former case, the first-order time derivative is replaced by a fractional derivative, making the problem global in time. We propose a spectral method in both temporal and spatial discretizations for this equation. The convergence of the method is proven by providing a… CONTINUE READING
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