Efficient yet accurate solution of the linear transport equation in the presence of internal sources: The exponential-linear-in-depth approximation (Q1201707)

Problems involving neutral or charge particle transport in a background medium and rarefied gas dynamics require solutions of a linear transport equation derivable from the Boltzmann equation. This paper deals with the search of a particular solution in the presence of a general internal source term. The source term is approximated by an exponential-polynomial function \(Q(\tau,\mu)=e^{-\alpha\tau}\sum^ k_{i=0}x_ i(\mu)\tau^ i\) and then the authors are looking for a particular solution of the form \(u_ p(\tau,\mu_ i)=e^{- \alpha\tau}\sum^ k_{j=0}y_ j(\mu_ i)\tau^ j\) where the \(y_ j(\mu_ i)\) are determined owing to a system of linear algebraic equations. A lot of numerical results are given proving that the numerical code is stable, computationally efficient and allows to solve a great variety of physical problems.