The Research Of Eigenvalue Numerical Solution Methods For Weakly Singular Integral Equation In L~1Space

Majority of practical problems in science and engineer can be solution andtransformed into the issue of eigenvalue in compact linear operator. In the theoryof integral equation, eigenvalue and eigenfunction is the core theory. There arefew cases for non-zero existence and uniqueness of eigenvalues and eigenfunction,and solving eigenvalue is very rare. The commonly used method of the solution ofthe eigenvalue is discreting integral operator into a matrix, and then solving theeigenvalues of the matrix, the eigenvalues of the matrix is thingking of the approx-imate solution of the integral operator eigenvalues. In order to more convenient,we explore integral equations eigenvalues deeply. This essay is aim to discussed theeigenvalues of weakly singular integral equation in L1space, which using iterativemethod to transform weakly singular integral equation into continuous kernel, thendiscrete the continuous kernel integral operator into matrix. The matrix charac-teristic root is the approximate eigenvalue of continuous nuclear integral operator,which makes the eigenvalue approximately can be known. To give the examples,using the character value issue of the integral operator with weakly singular kernelas the model, through the Matlab programming to make numerical test, calculatethe approximate numerical solution, so as to ensure the presented method is correctand practical. Using linear operators boundedness, existence,uniform continuityand spectral theory to prove the rationality of the algorithm. At last, Gives a weaksingularity kernel integral operator eigenvalue problem of the concrete example,make the numerical experiments by Matlab programming, work out the approx-imate numerical solutions of the example, verify the correctness and feasibility ofthe proposed algorithm.