Numerical solution of Fredholm integral equation of the first kind with collocation method and estimation of error bound

摘要

Fredholm integral equation of the first kind is one of the inverse problems that arise in many engineering fields such as image processing and electromagnetic. Most inverse problems are ill-posed, so that solving discretized system of such problems with large condition number has a lot of difficulties. In this paper with using wavelet basis and collocation method the integral equation reduce to a linear system of equation. Then for solving the system we use the CG method. Furthermore, we get an estimation of error bound for this method.