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High-order difference schemes based on new Marchuk integral identities for one-dimensional interface problems

High-order difference schemes based on new Marchuk integral identities for one-dimensional... High-order finite difference approximations of the solution and the flux to model interface problems in one-dimension are constructed and analyzed. Explicit formulas based on new Marchuk integral identities that give O ( h 2 ), O ( h 4 ),… accuracy are derived. Numerical integration procedures using Lobatto quadratures for computing three-point schemes of any prescribed order of accuracy are developed. A rigorous rate of convergence analysis is presented. Numerical experiments confirm the theoretical results. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Numerical Mathematics de Gruyter

High-order difference schemes based on new Marchuk integral identities for one-dimensional interface problems

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References (15)

Publisher
de Gruyter
Copyright
Copyright 2005, Walter de Gruyter
ISSN
1570-2820
eISSN
1569-3953
DOI
10.1515/1569395054068982
Publisher site
See Article on Publisher Site

Abstract

High-order finite difference approximations of the solution and the flux to model interface problems in one-dimension are constructed and analyzed. Explicit formulas based on new Marchuk integral identities that give O ( h 2 ), O ( h 4 ),… accuracy are derived. Numerical integration procedures using Lobatto quadratures for computing three-point schemes of any prescribed order of accuracy are developed. A rigorous rate of convergence analysis is presented. Numerical experiments confirm the theoretical results.

Journal

Journal of Numerical Mathematicsde Gruyter

Published: Apr 1, 2005

Keywords: Finite difference schemes,; integral identities,; interface problems

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