Numerical Solution of the Ambartsumian Functional Equations for a Plane Medium with Finite Thickness

A numerical algorithm is used to solve the Ambartsumian functional equations for a finite layer. Calculations are done for the special case of frequency redistribution of the radiation. To do this the program first calculates the nodes of Hermite polynomials and the corresponding weights using a pro...

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Bibliographic Details
Published in:Astrophysics 2018-12, Vol.61 (4), p.525-538
Main Authors: Harutyunian, H. A., Poghosyan, H. A.
Format: Article
Language:English
Subjects:
Analysis
Astronomical research
Astronomy
Astrophysics
Astrophysics and Astroparticles
Astrophysics and Cosmology
Digits
Functional equations
Hermite polynomials
Mathematical analysis
Methods
Nodes
Numerical analysis
Observations and Techniques
Optical thickness
Physics
Physics and Astronomy
Radiation
Radiative transfer
Space Exploration and Astronautics
Space Sciences (including Extraterrestrial Physics
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Description
Summary:A numerical algorithm is used to solve the Ambartsumian functional equations for a finite layer. Calculations are done for the special case of frequency redistribution of the radiation. To do this the program first calculates the nodes of Hermite polynomials and the corresponding weights using a program package that works with a large number of significant digits. The effect of the number of quadrature nodes, as well as of the optical thickness of the layer and the photon survival probability, on the final result of solving these equations is examined. As an illustration, some computational results are shown in the form of graphs and tables.
ISSN:0571-7256
1573-8191
DOI:10.1007/s10511-018-9555-4