A Fourth Order Finite Difference Approximation to the Eigenvalues Approximation to the Eigenvalues of a Clamped Plate (Journal of Computational Mathematics, 2018)
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.