Linearized BGK and neutron transport equations in finite domains

Abstract

A study is made of the integro-differential equation

For ψ(μ)=π^−½e^−μ2 this equation arises in the linearized BGK model; for ψ(μ)=½c(|μ|≤1), ψ(μ)=0(|μ|>1) it describes neutron transport in a slab with isotropic scattering. With the help of the existing theory of convolution equations solutions of various boundary value problems are obtained. The auxiliary functions appearing in the sesolutions are shown to satisfycerta in X- and Y - equations. Arational approximation method for the computation of the se X- and Y - functions is explored.