New variants of the collocation method for integral equations of the third kind (Q1178073)

Third kind integral equations appear in mass transport equations, elasticity equations, etc. In this paper a new variant of the collocation method is applied to a third kind integral equation. A uniqueness and existence theorem for the approximate solutions is proved and their convergence to the exact solution is shown. These investigations are based on Bernstein polynomials and on application of Hermite-Fourier polynomials.