A MULTISCALE MOMENT METHOD FOR SOLVING FREDHOLM INTEGRAL-EQUATION OF THE FIRST KIND - SUMMARY

The aim of this paper is to deal with the problem of numerical solutio n of Fredholm integral equation of the first kind. First, a new kind o f basis functions has been proposed based on multiscale method and wav elet-like basis. Second, by using this basis, the multiscale moment me thod for solving Fredholm integral equation of the first kind in one d imension has been proposed. Furthermore, the adaptive algorithm of the multiscale moment method has been presented according to the characte ristics of the integral equation. Many numerical simulations are carri ed out to test the feasibility of the multiscale method and the implem ented adaptive algorithm. It is found that the two multiscaling algori thms can provide good results. The adaptive algorithm can reduce the o rders of linear equations constructed by multiscale moment method for Fredholm integral equation. It is a very effective algorithm to solve integral equations.