A numerical study of the homogeneous elliptic equation with fractional boundary conditions
type: Item
instance of: scholarly article
title: A numerical study of the homogeneous elliptic equation with fractional boundary conditions
zbMATH Open document ID: 1364.65253
publication date: 2017-06-08T00:00:00Z
full work available at URL: https://arxiv.org/abs/1702.06477
review text: The authors consider the numerical approximation of homogeneous second order elliptic equations with boundary conditions involving fractional power \(\alpha\), with \(0<\alpha <1\), of the Steklov spectral operator arising in Dirichlet to Neumann map. Two numerical methods are presented and discussed. The first one is a computational algorithm based on an approximation of the integral representation of the fractional power of the operator, whereas the second one is based on the introduction of an auxiliary Cauchy problem for an ultra-parabolic equation and its subsequent approximation by a time stepping technique. Some numerical experiments are presented to justify the accuracy and stability of the algorithms for both methods.
reviewed by: Abdallah Bradji
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35R11
zbMATH DE Number: 6726943
zbMATH Keywords: fractional partial differential equations
zbMATH Keywords: fractional boundary conditions
zbMATH Keywords: numerical methods for fractional powers of elliptic operators
zbMATH Keywords: ultra-parabolic equations
author: Raytcho D. Lazarov
author: P. N. Vabishchevich
describes a project that uses: mftoolbox
MaRDI profile type: Publication
OpenAlex ID: W2963869779
arXiv ID: 1702.06477
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DOI: 10.1515/FCA-2017-0018
published in: Fractional Calculus \ Applied Analysis
description: scientific article