ACCELERATION TECHNIQUES BY POST-PROCESSING OF NUMERICAL SOLUTIONS OF THE HAMMERSTEIN EQUATION

In this paper, severed acceleration techniques for numerical solutions of the Hammerstein equation by post-processing are discussed. The paper is motivated by the results reported in papers [7, 8]. Results in these papers are concerned with certain post acceleration techniques for numerical solution...

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Bibliographic Details
Published in:The Journal of integral equations and applications 2011-12, Vol.23 (4), p.565-595
Main Authors: NEAMPREM, KHOMSAN, KANEKO, HIDEAKI
Format: Article
Language:English
Subjects:
Approximation
Degrees of polynomials
Differential equations
extrapolation technique
Galerkin methods
Hammerstein equations
Interpolation
Iterative methods
Mathematical extrapolation
Mathematics
Polynomials
Post-processing techniques
Textual collocation
the collocation method
the Galerkin method
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Summary:In this paper, severed acceleration techniques for numerical solutions of the Hammerstein equation by post-processing are discussed. The paper is motivated by the results reported in papers [7, 8]. Results in these papers are concerned with certain post acceleration techniques for numerical solutions of the second kind Fredholm integral equation. Techniques consist of interpolation post-processing and extrapolation. Post-processed solutions are shown to exhibit better accuracy. We propose in this paper to generalize the results in [7, 8] to nonlinear integral equations of the Hammerstein type. An extrapolation technique for the Galerkin solution of Hammerstein equation is also obtained. This result appears new even in the setting of the linear Fredholm equation.
ISSN:0897-3962
1938-2626
DOI:10.1216/JIE-2011-23-4-565