On the numerical solution of Cauchy singular integral equations in neutron transport

The use of Case eigen functions in the solution of Boltzmann equation for neutron transport results in an integral equation with a singular kernel. We show a solution prescription that combines a polynomial expansion for the unknown, a collocation procedure for fixing the expansion coefficients and a Double Exponential quadrature for the Cauchy principal value integral. For a set of test problems, we demonstrate the advantages of this method over the same procedure based on the TANH quadrature.