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A Fourth Order Finite Difference Approximation to the Eigenvalues Approximation to the Eigenvalues of a Clamped Plate
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@Article{JCM-6-267,
author = {Tao , LüLiem , Chin Bo and Shih , Tis Min},
title = {A Fourth Order Finite Difference Approximation to the Eigenvalues Approximation to the Eigenvalues of a Clamped Plate},
journal = {Journal of Computational Mathematics},
year = {1988},
volume = {6},
number = {3},
pages = {267--271},
abstract = {
In a 21-point finite difference scheme, assign suitable interpolation values to the fictitious node points. The numerical eigenvalues are then of $O(h^2)$ precision. But the corrected value $\hat{λ}_h=λ_h+\frac{h^2}{6}λ_h^{\frac{3}{2}}$ and extrapolation $\hatλ_h=\frac{4}{3}λ_{\frac{λ}{2}}-\frac{1}{3}λ_h$ can be proved to have $O(h^4)$ precision.
}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9515.html} }
TY - JOUR
T1 - A Fourth Order Finite Difference Approximation to the Eigenvalues Approximation to the Eigenvalues of a Clamped Plate
AU - Tao , Lü
AU - Liem , Chin Bo
AU - Shih , Tis Min
JO - Journal of Computational Mathematics
VL - 3
SP - 267
EP - 271
PY - 1988
DA - 1988/06
SN - 6
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/9515.html
KW -
AB -
In a 21-point finite difference scheme, assign suitable interpolation values to the fictitious node points. The numerical eigenvalues are then of $O(h^2)$ precision. But the corrected value $\hat{λ}_h=λ_h+\frac{h^2}{6}λ_h^{\frac{3}{2}}$ and extrapolation $\hatλ_h=\frac{4}{3}λ_{\frac{λ}{2}}-\frac{1}{3}λ_h$ can be proved to have $O(h^4)$ precision.
Tao Lü, Chin Bo Liem & Tis Min Shih. (1970). A Fourth Order Finite Difference Approximation to the Eigenvalues Approximation to the Eigenvalues of a Clamped Plate.
Journal of Computational Mathematics. 6 (3).
267-271.
doi:
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