An overview of numerical methods for the first kind Fredholm integral equation

Abstract

In the field of engineering technology, many problems can be transformed into the first kind Fredholm integral equation, which has a prominent feature called “ill-posedness”. This property makes it difficult to find the analytical solution of first kind Fredholm integral equation. Therefore, how to find the numerical solution of first kind Fredholm integral equation has been a common concern of domestic and overseas scholars in recent years. In this article, various numerical solution methods of first kind Fredholm integral equation are introduced in detail. First, the existence and convergence of the solution of the integral equation are given. Second, the current mainstream numerical methods, such as regularization method, wavelet analysis method and multilevel iteration method are introduced in detail. Finally, we presented a concise overview of the numerical method of first kind Fredholm integral equation.