Fractional Spectral Collocation Method

@article{Zayernouri2014FractionalSC,
  title={Fractional Spectral Collocation Method},
  author={Mohsen Zayernouri and George Em Karniadakis},
  journal={SIAM J. Sci. Comput.},
  year={2014},
  volume={36}
}
We develop an exponentially accurate fractional spectral collocation method for solving steady-state and time-dependent fractional PDEs (FPDEs). We first introduce a new family of interpolants, called fractional Lagrange interpolants, which satisfy the Kronecker delta property at collocation points. We perform such a construction following a spectral theory recently developed in [M. Zayernouri and G. E. Karniadakis, J. Comput. Phys., 47 (2013), pp. 2108--2131] for fractional Sturm--Liouville… 

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