Numerical solution of Fredholm integral equations of the first kind by using Legendre wavelets (Q876671)

The authors discuss the Legendre wavelet approach for approximating the solution of Fredholm integral equations of the first kind. The continuous Legendre wavelets constructed on \([0,1]\) are utilized as a basis in the Galerkin method to reduce the solution of linear integral equations to a system of algebraic equations. For solving this system, the author uses the conjugate gradient method. Furthermore, the authors discuss a convergence analysis and error estimation for this method. Finally, the authors give some numerical examples for showing the efficiency of this method.