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An application of Newton's method to differential and integral equations

Published online by Cambridge University Press:  17 February 2009

J. M. Gutiérrez  and
M. A. Hernández
J. M. Gutiérrez
Affiliation:
Department of Mathematics and Computation, University of La Rioja, C/ Luis de Ulloa s/n, 26004, Logroño, Spain.
M. A. Hernández
Affiliation:
Department of Mathematics and Computation, University of La Rioja, C/ Luis de Ulloa s/n, 26004, Logroño, Spain.
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Abstract

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Newton's method is applied to an operator that satisfies stronger conditions than those of Kantorovich. Convergence and error estimates are compared in the two situations. As an application, we obtain information on the existence and uniqueness of a solution for differential and integral equations.

Type
Research Article
Information
The ANZIAM Journal , Volume 42 , Issue 3 , January 2001 , pp. 372 - 386
Copyright
Copyright © Australian Mathematical Society 2001

References

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