A Slow Method For Solving Fredholm Integral Equations

The theory of differential equations inverse problems widespread in variousfields, especially mathematical physics equations were eventually attributed todifferential equations. And, the structural vibration inverse problem, can be reducedto solving the Fredholm integrale quation of the frist kind problem,though themethod of separating the function.Generally, the Fredholm integral equations of the frist kind is ill-posed,so it isdifficulte to solve. In order to stabilize solving Fredholm integral equation of thefrist kind, some of the methods of previous studies mainly is regularization method.this method the development of continuous optimization, to become the mainmethod for solving the Fredholm integral equation of the frist kind. No matter howwe improve and optimize the method of solving the Fredholm integral equation ofthe frist kind,It is only an approximate solution method.If we can calculated all possible function value, then we will be able to findthe most accurate solution. We study such data search method slowly to solvingFredholm integral equation of the frist kind. Although this method need to amountof calculation, and the speed is slow, after all, it is a precise solution and reliableway. And with the development of computers, the advantages of this method willbecome significant increasingly.Based on the above ideas, we do the following research:1. Slow data search method for solving the Fredholm integrale quation of thefrist kind; analysis of feasibility and stability;experiments numerical simulation.2. Numerical simulation experiments, as well as speed up the search: step-by-step search method.3.Application of data search method the Fredholm integrale quation of the fristkind in parameter Determination.