This investigation uses symbolic computation in developing analytical methods and general computational strategies for solving both linear and nonlinear, regular and singular, integral and integro-differential equations which appear in radiative and combined mode energy transport. This technical report summarizes the research conducted during the first nine months of the present investigation. The use of Chebyshev polynomials augmented with symbolic computation has clearly been demonstrated in problems involving radiative (or neutron) transport, and mixed-mode energy transport. Theoretical issues related to convergence, errors, and accuracy have also been pursued. Three manuscripts have resulted from the funded research. These manuscripts have been submitted to archival journals. At the present time, an investigation involving a conductive and radiative medium is underway. The mathematical formulation leads to a system of nonlinear, weakly-singular integral equations involving the unknown temperature and various Legendre moments of the radiative intensity in a participating medium. Some preliminary results are presented illustrating the direction of the proposed research.
Frankel, J.I.. The use of symbolic computation in radiative, energy, and neutron transport calculations. Technical report, 15 August 1992--14 August 1994. United States: N. p., 1995.
Web. doi:10.2172/81042.
Frankel, J.I.. The use of symbolic computation in radiative, energy, and neutron transport calculations. Technical report, 15 August 1992--14 August 1994. United States. doi:10.2172/81042.
Frankel, J.I.. Thu .
"The use of symbolic computation in radiative, energy, and neutron transport calculations. Technical report, 15 August 1992--14 August 1994". United States.
doi:10.2172/81042. https://www.osti.gov/servlets/purl/81042.
@article{osti_81042,
title = {The use of symbolic computation in radiative, energy, and neutron transport calculations. Technical report, 15 August 1992--14 August 1994},
author = {Frankel, J.I.},
abstractNote = {This investigation uses symbolic computation in developing analytical methods and general computational strategies for solving both linear and nonlinear, regular and singular, integral and integro-differential equations which appear in radiative and combined mode energy transport. This technical report summarizes the research conducted during the first nine months of the present investigation. The use of Chebyshev polynomials augmented with symbolic computation has clearly been demonstrated in problems involving radiative (or neutron) transport, and mixed-mode energy transport. Theoretical issues related to convergence, errors, and accuracy have also been pursued. Three manuscripts have resulted from the funded research. These manuscripts have been submitted to archival journals. At the present time, an investigation involving a conductive and radiative medium is underway. The mathematical formulation leads to a system of nonlinear, weakly-singular integral equations involving the unknown temperature and various Legendre moments of the radiative intensity in a participating medium. Some preliminary results are presented illustrating the direction of the proposed research.},
doi = {10.2172/81042},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Thu Jun 01 00:00:00 EDT 1995},
month = {Thu Jun 01 00:00:00 EDT 1995}
}