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

Author

Listed:
  • Dalmolin, D.
  • de Azevedo, F.S.
  • Sauter, E.

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.

Suggested Citation

  • Dalmolin, D. & de Azevedo, F.S. & Sauter, E., 2022. "Advances in the theory of existence and numerical simulations for the one-dimensional transport equation," Applied Mathematics and Computation, Elsevier, vol. 428(C).
    • Handle: RePEc:eee:apmaco:v:428:y:2022:i:c:s009630032200265x
    DOI: 10.1016/j.amc.2022.127191
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