On the stability of the spectral Galerkin approximation |
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Authors: | Lyashenko Andrei A |
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Institution: | (1) Department of Mathematics, Iowa State University, 400 Carver Hall, Ames, IA 50011, USA;(2) Institute of Mathematics, Novosibirsk, 630090, Russia |
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Abstract: | We study stability properties of the spectral Galerkin approximation of the solutions of semilinear problems. Assuming that
the data of the problem are known within a certain error, we investigate when the solution of the Galerkin approximate equation
provides a desired accuracy uniformly with respect to small perturbations of the data. We show that for certain classes of
semilinear problems an additional compactness assumption is sufficient to assure that the spectral Galerkin method provides
an accurate approximation to the exact solution uniformly with respect to small perturbations of the data.
This revised version was published online in June 2006 with corrections to the Cover Date. |
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Keywords: | |
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