A splitting scheme to solve an equation for fractional powers of elliptic operators
Numerical Analysis
2015-05-18 v1 Numerical Analysis
Abstract
An equation containing a fractional power of an elliptic operator of second order is studied for Dirichlet boundary conditions. Finite difference approximations in space are employed. The proposed numerical algorithm is based on solving an auxiliary Cauchy problem for a pseudo-parabolic equation. Unconditionally stable vector additive schemes (splitting schemes) are constructed. Numerical results for a model problem in a rectangle calculated using the splitting with respect to spatial variables are presented.
Keywords
Cite
@article{arxiv.1505.04103,
title = {A splitting scheme to solve an equation for fractional powers of elliptic operators},
author = {Petr N. Vabishchevich},
journal= {arXiv preprint arXiv:1505.04103},
year = {2015}
}
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18 pages