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Superconvergence of the iterated degenerate kernel method

Hiromasa Kaneko, Peter A. Padilla, Yuesheng Xu

Open publisher page 21 citations

Abstract

First, in this paper, a generally theory for the iterated operator approximation is developed. Some of the known results of the superconvergence of the various iterated schemes can be formulated as special cases of this theory. The method is then subsequently used to prove the superconvergence of the iterated degenerate kernel method for the Fredholm equations of the second kind. A similar result of the superconvergence of the degenerate kernel method for the Hammerstein equations is also given.

About this research paper

What this paper is about

First, in this paper, a generally theory for the iterated operator approximation is developed. Some of the known results of the superconvergence of the various iterated schemes can be formulated as special cases of this theory. The method is then subsequently used to prove the superconvergence of the iterated degenerate kernel method for the Fredholm equations of the second kind. A similar result of the superconvergence of the degenerate kernel method for the Hammerstein equations is also given.

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OpenAlex reports 21 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

First, in this paper, a generally theory for the iterated operator approximation is developed. Some of the known results of the superconvergence of the various iterated schemes can be formulated as special cases of this theory. The method is then subsequently used to prove the superconvergence of the iterated degenerate kernel method for the Fredholm equations of the second kind. A similar result of the superconvergence of the degenerate kernel method for the Hammerstein equations is also given.

Key concepts: Superconvergence, Mathematics, Iterated function, Degenerate energy levels, Kernel (algebra), Applied mathematics, Operator (biology), Mathematical analysis

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