Efficient method for solving the Boltzmann equation on a uniform mesh

A new numerical method for solving the Boltzmann equation on a uniform mesh in velocity space is proposed. The asymptotic complexity of the method is $O(N^3)$, where $N$ is the total number of nodes on a three-dimensional mesh. The algorithm is efficient on relatively small meshes due to the simplicity of its operations and easy parallelization. The method preserves the most important properties of the solution, such as nonnegativity and conservation of total energy, momentum, and the number of particles.