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Journal of Scientific Computing

Erschienen in:

01.10.2012

Recent Advances in the Study of a Fourth-Order Compact Scheme for the One-Dimensional Biharmonic Equation

verfasst von: D. Fishelov, M. Ben-Artzi, J.-P. Croisille

Erschienen in: Journal of Scientific Computing | Ausgabe 1/2012

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Abstract

It is well-known that non-periodic boundary conditions reduce considerably the overall accuracy of an approximating scheme. In previous papers the present authors have studied a fourth-order compact scheme for the one-dimensional biharmonic equation. It relies on Hermitian interpolation, using functional values and Hermitian derivatives on a three-point stencil. However, the fourth-order accuracy is reduced to a mere first-order near the boundary. In turn this leads to an “almost third-order” accuracy of the approximate solution. By a careful inspection of the matrix elements of the discrete operator, it is shown that the boundary does not affect the approximation, and a full (“optimal”) fourth-order convergence is attained. A number of numerical examples corroborate this effect.

Vorheriger Artikel New Analysis of the Du Fort–Frankel Methods

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Titel: Recent Advances in the Study of a Fourth-Order Compact Scheme for the One-Dimensional Biharmonic Equation
verfasst von: D. Fishelov
M. Ben-Artzi
J.-P. Croisille
Publikationsdatum: 01.10.2012
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 1/2012
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-012-9611-x

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