Document Type


Date of Degree

Fall 2017

Degree Name

PhD (Doctor of Philosophy)

Degree In

Applied Mathematical and Computational Sciences

First Advisor

Han, Weimin

First Committee Member

Ayati, Bruce

Second Committee Member

Jay, Laurent

Third Committee Member

Jorgensen, Palle

Fourth Committee Member

Zhu, Xueyu


The radiative transfer equation (RTE) models the transport of radiation through a participating medium. In particular, it captures how radiation is scattered, emitted, and absorbed as it interacts with the medium. This process arises in numerous application areas, including: neutron transport in nuclear reactors, radiation therapy in cancer treatment planning, and the investigation of forming galaxies in astrophysics. As a result, there is great interest in the solution of the RTE in many different fields.

We consider the energy dependent form of the RTE and allow media containing regions of negligible absorption. This particular case is not often considered due to the additional dimension and stability issues which arise by allowing vanishing absorption. In this thesis, we establish the existence and uniqueness of the underlying boundary value problem. We then proceed to develop a stable numerical algorithm for solving the RTE. Alongside the construction of the method, we derive corresponding error estimates. To show the validity of the algorithm in practice, we apply the algorithm to four different example problems. We also use these examples to validate our theoretical results.


Error Estimates, Integral Equations, Numerical Analysis, Partial Differential Equations, Radiative Transfer, Well-posedness


viii, 99 pages


Includes bibliographical references (pages 96-99).


Copyright © 2017 Kenneth Daniel Czuprynski