A Singularly Perturbed Boundary Value Problems with Fractional Powers of Elliptic Operators

Abstract

A boundary value problem for a fractional power $0<\epsilon <1$ of the second-order elliptic operator is considered. The boundary value problem is singularly perturbed when $\epsilon \to 0$. 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. The numerical results are presented for a model two-dimen\-sional boundary value problem with a fractional power of an elliptic operator. Our work focuses on the solution of the boundary value problem with $0<\epsilon \ll 1$.

arXiv comment12 pages, 1 figure. arXiv admin note: text overlap with arXiv:1510.08297, arXiv:1412.5706