arXiv subjects

Yanzhi Gui

Publications and source records attributed to Yanzhi Gui.

2 recordsLinked to original sources

arXiv2026

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

This work addresses a central challenge in the numerical analysis of the cutoff spatially homogeneous Boltzmann equation: the development of rigorously justified, accurate numerical schemes. We present (i) a novel Fourier spectral method for the equation with Maxwellian and hard potentials, (ii) the derivation of the first rigorous error estimates for the proposed schemes. Comprehensive numerical experiments validate the theory, confirming the predicted accuracy and illustrating the method's capability to capture solution dynamics, including the approach to equilibrium. The study thus provides a complete framework--from theoretical analysis to practical implementation--for the reliable computation of solutions to this foundational kinetic model.

math.NA↗

arXiv2025

Numerical analysis of the homogeneous Landau equation: approximation, error estimates and simulation

We construct a numerical solution to the spatially homogeneous Landau equation with Coulomb potential on a domain $D_L$ with N retained Fourier modes. By deriving an explicit error estimate in terms of $L$ and $N$, we demonstrate that for any prescribed error tolerance and fixed time interval $[0, T ]$, there exist choices of $D_L$ and $N$ satisfying explicit conditions such that the error between the numerical and exact solutions is below the tolerance. Specifically, the estimate shows that sufficiently large $L$ and $N$ (depending on initial data parameters and $T$) can reduce the error to any desired level. Numerical simulations based on this construction are also presented. The results in particular demonstrate the mathematical validity of the spectral method proposed in the referenced literature.

math.AP↗