Research On Numerical Solution Of Multidimensional First Kind Of Fredholm Integral Equation

The multidimensional first kind of Fredholm integral equation has been widely used in the fields of mathematical physics and science and technology.However,due to the ill-posed characteristics of such problems and the complexity of high-dimensional numbers,it brings great difficulties to the research.Therefore,it is of great and far-reaching significance to study the numerical solution method.This paper mainly studies the two-dimensional and three-dimensional first kind of Fredholm integral equations,and analyzes its numerical solution method.The genenral research work of the thesis is as follows:(1)Make detailed arrangements for the development status,existing problems and research work of the first kind of Fredholm integral equations at home and abroad,and give relevant preliminary knowledge.(2)Using the numerical integral formula,the two-dimensional and three-dimensional first kind of Fredholm integral equations are discretized into a linear system,and the detailed process is given.(3)The inverse problem of two important differential equations(heat conduction,Poisson equation)is classified into two-dimensional first kind of Fredholm integral equation.Two iterative algorithms based on Kryov subspace(RRGMRES,CGLS)are given,the calculation consequence were contrasted and researched.(4)The three-dimensional first kind of Fredholm integral equations are studied by using the maximum entropy regularization method and the v-method.Based on this,a numerical solution method for inverse problems of a three-dimensional heat conduction equation is given and numerical simulation is carried out.The comparison shows that the proposed methods is feasible and effective.