Аннотация:

A new numerical algorithm for solving Fredholm integral equations of the second kind is proposed on the segment [a,b] of the real axis. The solution is search in the form of a Padé approximant with indeterminate coefficients. A specific form of Padé approximant is found in an iterative process in which part of the expression of a nonlinear equation is taken from the previous iteration. By collocations of the approximate equation at specified points obtains an overdetermined system of linear equations with respect to the Padé approximant coefficients which is solved by applying the QR decomposition to the matrix of the linear system. Presented the results of numerical experiments on solving several equations for which are known results obtained by other methods. By comparing the results obtained by the proposed algorithm with results achieved by other methods shown it's advantage in accuracy of the approximate solution over the compared methods.