The Research And Application Of Solution Methods For Fredholm Integral Equation In L~1Space

Majority of practical problems in science and engineering can be transformedinto the issue of eigenvalue in compact linear integral operator. In order to a moreconvenient solution of numerical approximation usually adopted approximationmethod to solve equations, As the product of integral collocation method Galerkinmethod was used to calculate the integral calculation, the main difculties are cal-culated integral computation is time-consuming and increased dramatically withthe subdivision precision discrete equation. In these methods the integral equationof the existence and uniqueness of the solution can be proved, but can be solvedexactly Only rarely.Nystro(?)m approximation solutions of high precision combination method canovercome the difculties, but the calculation of Nystro(?)m Using the method of mul-tiple discrete approximate solution has large error. The least squares computationprocess is similar to the Galerkin method to solve the asymmetric nuclear error issmaller. Fredholm is required to generate multiple discrete error. This paper basedon the numerical solution of the second kind Fredholm integral equation in L1space and L1space with weak odd inquiry Discrete numerical method given in theliterature research part of the characteristic value of integral equations, and proveits rationality.This paper will improve the process of the discrete method has been given, andcompared with the conventional Nystro(?)m algorithm and least square algorithm forinstance by Matlab mapping are compared, showing the superiority of the newalgorithm. And then applied to the transverse rod bending critical force in thecalculation.