Superconvergence of a collocationtype method for simple turning points of Hammerstein equations
Author:
Sunil Kumar
Journal:
Math. Comp. 50 (1988), 385398
MSC:
Primary 65R20; Secondary 45G10
MathSciNet review:
929543
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Abstract: In this paper a simple turning point (, ) of the parameterdependent Hammerstein equation is approximated numerically in the following way. A simple turning point (, ) of an equivalent equation for is computed first. This is done by solving a discretized version of a certain system of equations which has (, ) as part of an isolated solution. The particular discretization used here is standard piecewise polynomial collocation. Finally, an approximation to is obtained by use of the (exact) equation The main result of the paper is that, under suitable conditions, the approximations to and are both superconvergent, that is, they both converge to their respective exact values at a faster rate than the collocation approximation (of ) does to .
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DOI:
http://dx.doi.org/10.1090/S00255718198809295431
PII:
S 00255718(1988)09295431
Article copyright:
© Copyright 1988
American Mathematical Society
