An Algorithm for the calculation of non-isotropic collision integral matrix elements of the non-linear Boltzmann equation by the use of recurrence relations

TL;DR

This paper presents a recursive algorithm for calculating non-isotropic collision integral matrix elements in the non-linear Boltzmann equation, applicable to various interaction laws and particle mass ratios.

Contribution

It introduces a new recursive method for computing non-isotropic matrix elements, expanding the computational tools for solving the Boltzmann equation.

Findings

Algorithm efficiently computes non-isotropic matrix elements.

Applicable to any interaction law and mass ratio.

Enables more accurate solutions of the Boltzmann equation.

Abstract

An algorithm for sequential calculation of non-isotropic matrix elements of the collision integral which are necessary for the solution of the non-linear Boltzmann equation by moment method is proposed. Isotropic matrix elements that we believe are known, are starting ones. The procedure is valid for any interaction law and any mass ratio of the colliding particles.