Galerkin Method to an Integral Equation in the Kinetic Theory

A Galerkin method is applied to a singular integral equation of fredholm type originated in the problem of the rarefied gas flow over a plane wall. The solution is expanded in a series of the Abramowitz function. The numerical calculations were carried out up to ten-terms expansions. The results show a good convergence of the series.The comparison is made with the previous work obtained by the moment method.