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Volume 16, Issue 6
ID-Wavelets Method for Hammerstein Integral Equations

Xianbiao Wang & Wei Lin

J. Comp. Math., 16 (1998), pp. 499-508.

Published online: 1998-12

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  • Abstract

The numerical solutions to the nonlinear integral equations of Hammerstein-type $$ y (t)=f (t)+\int^1_0 k (t, s) g (s, y (s)) ds, \quad t\in [0,1] $$ are investigated. A degenerate kernel scheme basing on ID-wavelets combined with a new collocation-type method is presented. The Daubechies interval wavelets and their main properties are briefly mentioned. The rate of approximation solution converging to the exact solution is given. Finally we also give two numerical examples.

  • Keywords

Nonlinear integral equation, interval wavelets, degenerate kernel.

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COPYRIGHT: © Global Science Press

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@Article{JCM-16-499, author = {Wang , Xianbiao and Lin , Wei}, title = {ID-Wavelets Method for Hammerstein Integral Equations}, journal = {Journal of Computational Mathematics}, year = {1998}, volume = {16}, number = {6}, pages = {499--508}, abstract = {

The numerical solutions to the nonlinear integral equations of Hammerstein-type $$ y (t)=f (t)+\int^1_0 k (t, s) g (s, y (s)) ds, \quad t\in [0,1] $$ are investigated. A degenerate kernel scheme basing on ID-wavelets combined with a new collocation-type method is presented. The Daubechies interval wavelets and their main properties are briefly mentioned. The rate of approximation solution converging to the exact solution is given. Finally we also give two numerical examples.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9177.html} }
TY - JOUR T1 - ID-Wavelets Method for Hammerstein Integral Equations AU - Wang , Xianbiao AU - Lin , Wei JO - Journal of Computational Mathematics VL - 6 SP - 499 EP - 508 PY - 1998 DA - 1998/12 SN - 16 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9177.html KW - Nonlinear integral equation, interval wavelets, degenerate kernel. AB -

The numerical solutions to the nonlinear integral equations of Hammerstein-type $$ y (t)=f (t)+\int^1_0 k (t, s) g (s, y (s)) ds, \quad t\in [0,1] $$ are investigated. A degenerate kernel scheme basing on ID-wavelets combined with a new collocation-type method is presented. The Daubechies interval wavelets and their main properties are briefly mentioned. The rate of approximation solution converging to the exact solution is given. Finally we also give two numerical examples.

Wang , Xianbiao and Lin , Wei. (1998). ID-Wavelets Method for Hammerstein Integral Equations. Journal of Computational Mathematics. 16 (6). 499-508. doi:
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