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arXiv · 1402.1636

Numerical solving the boundary value problem for fractional powers of elliptic operators

Petr N. Vabishchevich
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Abstract

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 operator. The dependence of accuracy on grids in time and in space is studied.

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Petr N. Vabishchevich. 2014-02-07. Numerical solving the boundary value problem for fractional powers of elliptic operators. https://doi.org/10.1016/j.jcp.2014.11.022

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