Research of Tikhonov Regularization Method for Solving the First Type Fredholm Integral Equation

Abstract

Inverse problem is a relatively new area. The first type Fredholm integral equation is a special kind of inverse problem. A large number of inverse problems of mathematical physics have been translated into the first type Fredholm integral equation to solve the problem of computing. The first type Fredholm integral equation, ill-posedness of the problem is widespread. To ensure a stable numerical solution, this article introduces the concept and the relationship between them on the solution of inverse problems and the first type Fredholm integral equation and the reasons for the difficulty are caused as a result of its ill-posedness. Followed by the introduction is method to solve ill-posed problems theory, which describes the specific methods of regularization. Then introduce the process of solving the first type Fredholm integral equation. Approximate solution obtained through the regularization method. To compare with the exact solution was found: the first type Fredholm integral equation for the results of precision has been improved through the regularization method.