On the determination of optimal nodes and weight factors for the solution of completely incoherent scattering problem

For the numerical solution of the radiative transfer equation with complete redistribution of frequencies, it is necessary to select nodes and weight factors close to optimal, which provide the greatest proximity $\delta$ between the exact and approximate solutions. The issue is reduced to a discrete boundary-value problem. We prove the theorem of existence and uniqueness of solution for above discrete boundary-value problem. We show that this solution imparts minimum to the function $\delta.$ At the end of the work we give examples representing interest in radiative transfer theory of light and gamma quanta.