ID-Wavelets Method for Hammerstein Integral Equations

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.