Convergence of the collocation method for the integral Lippmann - Schwinger equation

Background. The aim of this work is to prove the convergence of the collocation method for Lippmann-Schwinger integral equations. Material and methods. The concepts of p-convergence in Banach spaces were used, the proper convergence of operators was implied, as well as elements of the theory of Fredholm integral operators. Results. The collocation method is formulated for the Fredholm integral equations of the second kind in bounded two- and three-dimensional domains; the convergence of the collocation method for integral equations in the space of continuous functions is proved; the uniform convergence of approximate solutions to exact solutions of the equations is established. Conclusions. The results obtained make it possible to substantiate the applicability of the collocation method for integral equations arising in the diffraction theory.