# A Spectral Approach for Solving the Nonclassical Transport Equation

## TL;DR

This paper presents a spectral method using Laguerre polynomials to numerically solve the nonclassical transport equation, enabling deterministic solutions for particle transport in complex systems.

## Contribution

It introduces a novel spectral approach that transforms the nonclassical transport equation into a classical form using Laguerre polynomial expansion.

## Key findings

- Validated the spectral method with numerical results in slab geometry.
- Demonstrated effectiveness for both classical and nonclassical transport problems.
- Provided a new deterministic solution technique for nonclassical particle transport.

## Abstract

This paper introduces a mathematical approach that allows one to numerically solve the nonclassical transport equation in a deterministic fashion using classical numerical procedures. The nonclassical transport equation describes particle transport for random statistically homogeneous systems in which the distribution function for free-paths between scattering centers is nonexponential. We use a spectral method to represent the nonclassical flux as a series of Laguerre polynomials in the free-path variable $s$, resulting in a nonclassical equation that has the form of a classical transport equation. We present numerical results that validate the spectral approach, considering transport in slab geometry for both classical and nonclassical problems in the discrete ordinates formulation.