Mathematical modelling and numerics of opinion consensus and polarisation dynamics

Abstract

This thesis investigates the application of the Boltzmann equation to opinion consensus and polarization dynamics. Building on classical kinetic gas theory, we examine opinion models that incorporate agent-specific variables, such as external diffusion and compromise propensity, to describe social interactions. To solve the governing equations, we develop and implement Direct Simulation Monte Carlo (DSMC) algorithms for the homogeneous Boltzmann equation. The numerical scheme is extensively studied and subsequently applied to simulate and analyze the proposed opinion dynamics.