A Fourier spectral method for the cutoff Boltzmann equation: Convergence analysis and numerical simulation

Abstract

This work presents a novel Fourier spectral method for the cutoff spatially homogeneous Boltzmann equation with Maxwellian and hard potentials. We establish finite-time error estimates in a weighted whole-space $L^2$ norm, with explicit dependence on the velocity cutoff $R$ and the number of Fourier modes $N$.