On second order of accuracy difference scheme of the approximate solution of nonlocal elliptic-parabolic problems
type: Item
instance of: scholarly article
title: On second order of accuracy difference scheme of the approximate solution of nonlocal elliptic-parabolic problems
zbMATH Open document ID: 1198.65120
DOI: 10.1155/2010/705172
author: Allaberen Ashyralyev
author: Okan Gercek
published in: Abstract and Applied Analysis
publication date: 2010-09-27T00:00:00Z
full work available at URL: https://eudml.org/doc/230408
review text: Summary: A second order of accuracy difference scheme for the approximate solution of the abstract nonlocal boundary value problem \( - d^{2}u(t)/dt^{2}+Au(t)=g(t), (0\leq t\leq 1), du(t)/dt - Au(t)=f(t), ( - 1\leq t\leq 0), u(1)=u( - 1)+\mu \) for differential equations in a Hilbert space \(H\) with a self-adjoint positive definite operator \(A\) is considered. The well posedness of this difference scheme in Hölder spaces is established. In applications, coercivity inequalities for the solution of a difference scheme for elliptic-parabolic equations are obtained and a numerical example is presented.
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 35M13
Mathematics Subject Classification ID: 65M06
zbMATH DE Number: 5791635
zbMATH Keywords: difference scheme
zbMATH Keywords: abstract nonlocal boundary value problem
zbMATH Keywords: Hilbert space
zbMATH Keywords: self-adjoint positive definite operator
zbMATH Keywords: well posedness
zbMATH Keywords: Hölder spaces
zbMATH Keywords: elliptic-parabolic equations
zbMATH Keywords: numerical example
Wikidata QID: Q58649906
MaRDI profile type: Publication
OpenAlex ID: W2156827765
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description: scientific article; zbMATH DE number 5791635