Skip to main content
SpringerLink
Log in

The calculation of Sobolev's ϕ function of radiative transfer via numerical inversion of Laplace transforms

  • Published:
CALCOLO Aims and scope Submit manuscript

Abstract

The linear integral equation of convolution type of Sobolev's function ϕ is solved computationally using a new method for the numerical inversion of Laplace transforms.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Sobolev, V.,A Treatise on Radiative Transfer, D. Van Nostrand and Company, Inc., Princeton, 1963.

    Google Scholar 

  2. Ambartsumian, V., «Diffuse Reflection of Light by a Foggy Medium»,Doklady Akad. Nauk SSSR,38 (1943), 229–232.

    Google Scholar 

  3. Chandrasekhar, S.,Radiative Transfer Dover Publications, Inc., New York, 1960.

    Google Scholar 

  4. Bellman, R., H. Kagiwada, R. Kalaba andM. Prestrud,Invariant Imbedding and Time-Dependent Transport Processes, American Elsevier Publishing Company, Inc., New York, 1964.

    MATH  Google Scholar 

  5. Bellman, R., H. Kalaba andJ. Lockett,Numerical Inversion, of Laplace Transforms with Applications, American Elsevier Publishing Company, Inc., New York, 1966.

    Google Scholar 

  6. Bellman, R., H. Kagiwada, R. Kalaba andS. Ueno, «Numerical Results for Chandrasekhar'sX andY Functions of Radiative Transfer», to appear inJ. Quantitative Spectroscopy and Radiative Transfer.

  7. Kagiwada, H. andR. Kalaba,Numerical Results for Internal Intensities in Atmospheres Illuminated by Isotropic Sources, The RAND Corporation, RM-4958-PR, April 1966.

  8. Stibbs, D. andR. Weir, «On theH-Function for Isotropic Scattering»,Monthly Notices,119 (1959), 512–525.

    MATH  MathSciNet  Google Scholar 

  9. Minin, I. «On the Theory of the Diffusion of Radiation in a Semi-Infinite Medium»,Soviet Physics Doklady,3 (1958), 535–537.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Rand Corporation, St. Monica, USA

    H. Kagiwada & R. Kalaba

Authors
  1. H. Kagiwada
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Kalaba
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This research is sponsored by the United States Air Force under Project RAND —Contract No. AF 49 (638), 1700—monitored by the Directorate of Operational Requirements and Development Plans, Deputy Chief of Staff, Research and Development Hq, USAF. Views or conclusions contained in this paper should not be interpreted as representing the official opinion or policy of the United States Air Force.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kagiwada, H., Kalaba, R. The calculation of Sobolev's ϕ function of radiative transfer via numerical inversion of Laplace transforms. Calcolo 4, 11–20 (1967). https://doi.org/10.1007/BF02641642

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02641642

Keywords

Search

Navigation