Numerically solving an equation for fractional powers of elliptic operators

@article{Vabishchevich2015NumericallySA,
  title={Numerically solving an equation for fractional powers of elliptic operators},
  author={Petr N. Vabishchevich},
  journal={J. Comput. Physics},
  year={2015},
  volume={282},
  pages={289-302}
}
A boundary value problem for a fractional power of the second-order elliptic operator is considered. It is solved numerically using a time-dependent problem for a pseudo-parabolic equation. For the auxiliary Cauchy problem, the standard two-level schemes with weights are applied. Stability conditions are obtained for the fully discrete schemes under the consideration. The numerical results are presented for a model two-dimensional boundary value problem wit a fractional power of an elliptic… CONTINUE READING
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