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Advances in Applied Mathematics and Approximation Theory pp 121–148Cite as

Theory of Differential Approximations of Radiative Transfer Equation

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 41))

Abstract

The radiative transfer equation (RTE) arises in a variety of applications. The equation is challenging to solve numerically for a couple of reasons: high dimensionality, integro-differential form, highly forward-peaked scattering in application. In the literature, various approximations of RTE have been proposed in the literature. In an earlier publication, we explored a family of differential approximations to RTE, to be called RT/DA equations. In this paper, we study the RT/DA equations and investigate numerically the closeness of solutions of the RT/DA equations to that of the RTE.

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Author information

Authors and Affiliations

  1. Department of Mathematics & Program in Applied Mathematical and Computational Sciences, University of Iowa, Iowa City, IA, 52242, USA

    Weimin Han & Qiwei Sheng

  2. Department of Mathematics, Rose-Hulman Institute of Technology, Terre Haute, IN, 47803, USA

    Joseph A. Eichholz

Authors
  1. Weimin Han
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  2. Joseph A. Eichholz
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  3. Qiwei Sheng
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Corresponding author

Correspondence to Weimin Han .

Editor information

Editors and Affiliations

  1. , Department of Mathematical Sciences, The University of Memphis, Memphis, 38152, Tennessee, USA

    George A. Anastassiou

  2. , Department of Mathematics, TOBB Economics and Technology University, Sögütözü, Ankara, 06530, Turkey

    Oktay Duman

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Han, W., Eichholz, J.A., Sheng, Q. (2013). Theory of Differential Approximations of Radiative Transfer Equation. In: Anastassiou, G., Duman, O. (eds) Advances in Applied Mathematics and Approximation Theory. Springer Proceedings in Mathematics & Statistics, vol 41. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6393-1_8

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