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The numerical solution of Hammerstein equations by a method based on polynomial collocation

Published online by Cambridge University Press:  17 February 2009

Sunil Kumar
Sunil Kumar
Affiliation:
School of Mathematics, The University of New South Wales, Sydney, NSW 2033, Australia.
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Abstract

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In recent papers we have considered the numerical solution of the Hammerstein equation

by a method which first applies the standard collocation procedure to an equivalent equation for z(t):= g(t, y(t)), and then obtains an approximation to y by use of the equation

In this paper we approximate z by a polynomial zn of degree ≤ n − 1, with coefficients determined by collocation at the zeros of the nth degree Chebyshev polynomial of the first kind. We then define the approximation to y to be

and establish that, under suitable conditions, , uniformly in t.

Type
Research Article
Information
The ANZIAM Journal , Volume 31 , Issue 3 , January 1990 , pp. 319 - 329
Copyright
Copyright © Australian Mathematical Society 1990

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