A Multiscale Moment Method for Solving Fredholm Integral Equation of the First Kind - Summary

Abstract

The aim of this paper is to deal with the problem of numerical solution of Fredholm integral equation of the first kind. First, a new kind of basis functions has been proposed based on multiscale method and wavelet-like basis. Second, by using this basis, the multiscale moment method for solving Fredholm integral equation of the first kind in one dimension has been proposed. Furthermore, the adaptive algorithm of the multiscale moment method has been presented according to the characteristics of the integral equation. Many numerical simulations are carried out to test the feasibility of the multiscale method and the implemented adaptive algorithm. It is found that the two multiscaling algorithms can provide good results. The adaptive algorithm can reduce the orders of linear equations constructed by multiscale moment method for Fredholm integral equation. It is a very effective algorithm to solve integral equations.