# [J8] The nonclassical Boltzmann equation and diffusion-based approximations to the Boltzmann equation

### Journal article

Martin Frank, Kai Krycki, Edward W. Larsen, Richard Vasques

Siam Journal on Applied Mathematics, vol. 75(3), 2015, pp. 1329-1345

Siam Journal on Applied Mathematics, vol. 75(3), 2015, pp. 1329-1345

DOI:
10.1137/140999451

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### Cite

**APA**

Frank, M., Krycki, K., Larsen, E. W., & Vasques, R. (2015). [J8] The nonclassical Boltzmann equation and diffusion-based approximations to the Boltzmann equation. Siam Journal on Applied Mathematics, 75(3), 1329–1345.

**Chicago/Turabian**

Frank, Martin, Kai Krycki, Edward W. Larsen, and Richard Vasques. “[J8] The Nonclassical Boltzmann Equation and Diffusion-Based Approximations to the Boltzmann Equation.” Siam Journal on Applied Mathematics 75, no. 3 (2015): 1329–1345.

**MLA**

Frank, Martin, et al. “[J8] The Nonclassical Boltzmann Equation and Diffusion-Based Approximations to the Boltzmann Equation.” Siam Journal on Applied Mathematics, vol. 75, no. 3, 2015, pp. 1329–45.

**ABSTRACT:**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.