Some remarks on fixed point and Newton techniques for solving the S2 approximation of transient radiative transfer

  • M. Falcone
  • Ó. López Pouso
Conference paper


We propose two numerical algorithms for solving the transient 1D radiative transfer equations in the slab: a fixed point algorithm and a Newton algorithm. The first one shows good behavior for optically thin media, but its convergence may fail otherwise; this limit is overcome with the second algorithm, which converges in all situations, and moreover is faster when the implementation presented here is used.


Newton Algorithm Internal Heat Source Fixed Point Algorithm Implicit Euler Scheme Thin Medium 


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    Falcone, M., López Pouso, O.: Analysis and comparison of two approximation schemes for a radiative transfer system. Math. Models Methods Appl. Sci., to appearGoogle Scholar
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    Modest, M.F. (1993): Radiative heat transfer. McGraw-Hill Inc., New YorkGoogle Scholar
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    Ortega, J.M., Rheinboldt, W.C. (1970): Iterative solution of nonlinear equations in several variables. Academic Press, New YorkMATHGoogle Scholar
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    Siegel, R. (1998): Transient effects of radiative transfer in semitransparent materials. Internat. J. Eng. Sci. 36, 1701–1739CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Italia 2003

Authors and Affiliations

  • M. Falcone
    • 1
  • Ó. López Pouso
    • 2
  1. 1.Dipartimento di MatematicaUniversità di Roma “La Sapienza”RomaItaly
  2. 2.Departamento de Matemática AplicadaUniversidade de Santiago de CompostelaSantiago de Compostela, A CoruñaSpain

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