A collocation method is formulated and justified for numerical solution of the Fredholm second-kind integral equations. As an application the Lippmann-Schwinger equation is considered. The results obtained provide an error estimate and a justification of the limiting procedure used in the earlier papers by the author, dealing with many-body scattering problems in the case of small scatterers, and with creating materials with a desired refraction coefficient: Ramm, A.G. 'Many-body wave scattering by small bodies and applications', J. Math. Phys., Vol. 48, No. 10, 103-511; Ramm, A.G. (2008) 'Wave scattering by many small particles embedded in a medium', Phys. Lett. A, Vol. 372, No. 17, (2008), pp.3064-3070