Matrix Riccati Equation Solution of the 1D Radiative Transfer Equation

Barry D. Ganapol, Japan Patel

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


In recent years, the first author has developed three successful numerical methods to solve the 1D radiative transport equation yielding highly precise benchmarks. The second author has shown a keen interest in novel solution methodologies and an ability for their implementation. Here, we combine talents to generate yet another high precision solution, the Matrix Riccati Equation Method (MREM). MREM features the solution to two of the four matrix Riccati ODEs that arise from the interaction principle of particle transport. Through interaction coefficients, the interaction principle describes how particles reflect from- and transmit through- a single slab. On combination with Taylor series and doubling, a high-quality numerical benchmark, to nearly seven places, is established.

Original languageEnglish (US)
Pages (from-to)297-327
Number of pages31
JournalJournal of Computational and Theoretical Transport
Issue number5
StatePublished - 2021


  • Cloud C1 and HAZE L phase functions
  • Interaction principle
  • benchmarks
  • doubling

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Transportation
  • General Physics and Astronomy
  • Applied Mathematics


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