Asymptotic Error Expansions for Numerical Solutions of Integral Equations |
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Authors: | MCLEAN W |
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Institution: |
School of Mathematics, University of New South Wales Sydney 2033, Australia
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Abstract: | A general theorem dealing with asymptotic error expansions fornumerical solutions of linear operator equations is proved.This is applied to the Nystr?m, collocation, and Galerkin methodsfor second kind, Fredholm integral equations. For example, weshow that when piecewise polynomials of degree m1 areused, the iterated Galerkin solution admits an error expansionin even powers of the step-size h, beginning with a term inh2m. |
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