Superconvergence of the iterated degenerate kernel method

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.

Keywords:

• The iterated degenerate kernel method;
• Fredholm integral equations of the second kind

AMS Classification:

• 65B05
• 45L10

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^∗Corresponding author.

Notes

^∗Corresponding author.