The Nonclassical Boltzmann Equation and DIffusion-Based Approximations to the Boltzmann Equation

We show that several diffusion-based approximations (classical diffusion or SP₁, SP₂, SP₃) to the linear Boltzmann equation can (for an infinite, homogeneous medium) be represented exactly by a nonclassical transport equation. As a consequence, we indicate a method to solve these diffusion-based approximations to the Boltzmann equation via Monte Carlo methods, with only statistical errors---no truncation errors.