Research On Improved Galerkin Algorithm For Two Kinds Of Fredholm Integral Equations

With the progress of science and technology,study on solving physics and Engineering in the field of the final lot can be attributed to the integral equation,but these integral equations usually it is very difficult to get the accurate solution,so how to find the integral equation for a more accurate numerical solution becomes the main research in the mathematics calculation to one of the.This paper is mainly based on the classical Galerkin method and proposes some improved algorithms.The improved Galerkin method is applied to solve second kinds of Fredholm integral equations.Based on the classical Galerkin method,the orthogonal Legendre wavelet basis functions are used to replace the general orthogonal basis functions.The function can be characterized by the orthogonal Legendre wavelet basis function,and then the inner product operation.In this paper,the specific algorithm steps are given,and numerical examples show that the accuracy of the method is higher than that of the classical Galerkin method.At the same time,with the Second Ferdholm hypersingular kernel of numerical solution of integral equation,we construct a reduced order method,by this method we have with the second Fredholm nuclear hypersingular integral equation is transformed into singular kernel Cauchy with the second kind of Fredholm integral,then carries on the numerical calculation using the improved Galerkin algorithm established.The implementation process of the algorithm is given in this paper,and the numerical example shows that the constructed numerical method is an effective algorithm.