Chebyshev-Hilbert transform method of solving a singular integral equation

Starting from the integral form of the transport equation and using the G-transform defined earlier, the singular integral equation for the flux in the angle variable is obtained. These singular integral equations for the full infinite medium and the semi infinite medium and other benchmark singular integral equations are solved by the Chebyshev-Hilbert transform method. Solutions are obtained in an extremely simple way and to a high degree of accuracy with or without resorting to rational approximations. Problems of finite media are also explored. (author). 4 refs., 5 tabs