The collocation method for Hammerstein equations by Daubechies wavelets

The numerical solutions to the nonlinear integral equations of Hammerstein-typey(t)=f(t)+∫01k(t,s)g(s,y(s))ds,t∈[0,1]with using Daubechies wavelets are investigated. A general kernel scheme basing on Daubechies wavelets combined with a collocation method is presented. The approach of creating Daubechies interval wavelets and their main properties are briefly mentioned. Also we present an algorithm for computing of Daubechies wavelets in collocation points. The rate of approximation solution converging to the exact solution is given. Finally we also give some numerical examples for showing efficiency of the method.