Chandrasekhar polynomials and the solution to the transport equation in an infinite medium

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Abstract

The Chandrasekhar polynomial of the first kind is at the heart of analytical solutions to the neutron and radiative transport equations in finite and infinite media. They form the basis for 1D solutions in plane geometry, which, in turn, enables solutions in spherical and cylindrical geometries. The scalar flux for a point source in spherical geometry permits scalar flux benchmarks for 2D and 3D sources in infinite media. The establishment of benchmarks expressly requires these polynomials to be highly accurate. Here, we focus on the numerical evaluation of Chandrasekhar polynomials for full anisotropic scattering as solutions to a three—term recurrence. When considered in this way, numerical theory guides their evaluation.

Original languageEnglish (US)
Pages (from-to)433-473
Number of pages41
JournalJournal of Computational and Theoretical Transport
Volume43
Issue number1-7
DOIs
Publication statusPublished - 2014

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Keywords

  • Chandrasekhar polynomials
  • Green’s function
  • Infinite medium
  • Three-term recurrence

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Transportation
  • Physics and Astronomy(all)
  • Applied Mathematics

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