A finite volume method for the Fermi pencil-beam equation

Paper in proceeding, 2021

The paper deals with the development and analysis of a finite volume computational method for the 2-D Fermi pencil-beam equation. The Fermi pencil-beam equation de- scribes the broadening of a monoenergetic, forward-peaked, particle beam in an optically thick system where the mean scattering angle is small and the large-angle scattering is negligible. This beam type appears in many applications such as radiation cancer ther- apy. In this work, explicit and implicit finite volume schemes for the Fermi equation are developed. Stability bounds are then provided and the convergence of the approximate solution to the weak solution of the problem is shown. Results of a numerical implemen- tation support the theoretical findings and verify the robustness of the method.