Advances in the theory of existence and numerical simulations for the one-dimensional transport equation

D. Dalmolin, F.S. de Azevedo and E. Sauter

Applied Mathematics and Computation, 2022, vol. 428, issue C

Abstract: The steady-state transport equation with internal sources and semi-reflective boundaries in a participative medium in slab geometry was analytically and numerically solved in this work. The existence theory in Hölder spaces when the sources belong to the space of continuous functions were established, generalizing results of previous works. Also, the Nyström method combines with singularity removal techniques was applied to produce an algorithm for calculating the scalar flux and criticality. The analytical estimates and the numerical methodology were obtained by looking at integral formulation as a Fredholm equation of the second type. Tabulated numerical results show the efficiency of the proposed methodology.

Keywords: Transport theory; Integral formulation; Existence theory; Nyström method; Fredholm equation (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S009630032200265X
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:428:y:2022:i:c:s009630032200265x

DOI: 10.1016/j.amc.2022.127191

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().