Numerical Solution of First Kind Fredholm Integral Equations Using Wavelet Collocation Method

We developed an algorithm based on combination of regularization and wavelet collocation method to solve Fredholm integral equations of the first kind. As first kind Fredholm integral equations are often ill-posed problems, regularization method is implemented to convert it into an approximate well posed Fredholm integral equation of the second kind whose solution converges to the solution of the original problem. Then wavelet collocation method is applied to obtain the numerical solution of the resulting problem. We have applied proposed method using Legendre and Chebyshev wavelets to some examples and compared their efficiency.