Astronomy and Astrophysics – Astrophysics
Scientific paper
Nov 1984
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984ap%26ss.106..355i&link_type=abstract
Astrophysics and Space Science (ISSN 0004-640X), vol. 106, no. 2, Nov. 1984, p. 355-369.
Astronomy and Astrophysics
Astrophysics
Albedo, Hamiltonian Functions, Kernel Functions, Transport Theory, Eigenvalues, Fredholm Equations, Taylor Series
Scientific paper
Das Gupta represented the H-functions of transport problems for the albedo w E [0, 1] in the form H(z) = R(z) - S(z) (see Das Gupta, 1977) where R(z) is a rational function of z and S(z) is regular on - 1, O]c. In this paper we have represented S(z) through a Fredhoim integral equation of the second kind with a symmetric real kernel L(y, z) as S(z) = f(z) - ~ L(y, z)S(y) dy. The problem is then solved as an eigenvalue problem. The kernel is converted into a degenerate kernel through finite Taylor's expansion and the integral equation for S(z) takes the form: S(z) = f(z) - x ~ F1(z)F,(y)S(y) dy (which is solved by the usual procedure) where Xr'S are the discrete eigenvalues and Fr'S the corresponding eigenfunctions of the real symmetric kernel L(y, z)
Das Gupta Santi Ranjan
Islam Zahirul
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