SINGULAR SOLUTIONS OF AN INTEGRO-DIFFERENTIAL EQUATION IN RADIATIVE TRANSFER
RAND CORP SANTA MONICA CA
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In the theory of radiative transfer in a homogeneous isotropic slab of thickness r the scattering reflection function can be determined by a nonlinear integro-differential equation and initial conditions. For a numerical analysis of this equation it is often important to know the behaviour of solutions in the vicinity of the desired solution. We extend in this Memorandum our previous treatment, Rl-3548-PR, of conservative and isotropic scattering to the nonconservative case. We exhibit a set of initial conditions for which the solutions to our nonlinear integro-differential equation are infinite for finite values of the parameter T. Some of these singular solutions first come close to the desired solution and then diverge to infinity. The nearness of approach of these singular solutions is proportional to a quantity which measures the nearness of local scattering to the conservative case. The conservative case is again found by a continuous passage from nonconservative to conservative scattering.
- Radioactivity, Radioactive Wastes and Fission Products