C. Tezcan et al., A NEW APPROACH OF SOLVING THE 3RD FORM OF THE TRANSPORT-EQUATION IN PLANE GEOMETRY - HALF-SPACE ALBEDO-PROBLEM, Journal of quantitative spectroscopy & radiative transfer, 55(2), 1996, pp. 251-258
In a new approach of solving the third form of the transport equation,
one should consider and compare the two methods C-N and F-N. Both of
the methods depend on the use of Green's function. In C-N method the G
reen's function obtained by the Fourier-transform technique is used to
solve the system of integral equations which is provided at the bound
ary of the various media. In F-N method which is a modified version of
C-N method. The Green's function in terms of singular eigenfunctions
is used to solve the integro-differential form of the Boltzmann equati
on. In our approach we use the Green's function of F-N method to solve
C-N equations. That is Green's function in terms of singular eigenfun
ctions is used to solve the system of integral equations of C-N method
. As in F-N method this approach yields simple analytical equations th
at can be solved numerically even more efficiently than the C-N method
and the convergence of the numerical results is faster than the numer
ical results of F-N method.