The nonlinear Boson diffusion equation (NBDE) is taken as a basis to account for the fast thermalization of gluons in the initial stages of relativistic heavy-ion collisions. For constant drift and diffusion coefficients and schematic initial conditions, this equation can be solved exactly. However, in order to achieve a more realistic time evolution towards thermalization, energy-dependent transport coefficients are necessary, requiring numerical solutions of the nonlinear equation. This talk describes the physical motivation for energy-dependent transport coefficients, showcases the differences between both approaches, and compares analytical and numerical solutions.