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Convergence Estimates for Galerkin Methods for Variable Coefficient Initial Value Problems

Vidar Thomee and Burton Wendroff
SIAM Journal on Numerical Analysis
Vol. 11, No. 5 (Oct., 1974), pp. 1059-1068
Stable URL: http://www.jstor.org/stable/2156042
Page Count: 10
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Convergence Estimates for Galerkin Methods for Variable Coefficient Initial Value Problems
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Abstract

The use of Galerkin's method for the approximate solution of the initial value problem for certain simple equations ∂ u/∂ t = Pu, where P is a differential operator of order m with respect to x, is analyzed when the approximate solution is sought in the space of smooth splines of order μ based on a uniform mesh with mesh-width h. It is proved that at the mesh-points the error can be made to be O(hν), where ν = 2μ - m for m even, ν = 2μ - m + 1 for m odd.

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