Volume 6, Issue 3
A Fourth Order Finite Difference Approximation to the Eigenvalues Approximation to the Eigenvalues of a Clamped Plate

J. Comp. Math., 6 (1988), pp. 267-271.

Published online: 1988-06

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• 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.

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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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