International Conference «Mathematical and Informational Technologies, MIT-2013»

(X Conference «Computational and Informational Technologies for Science,

Engineering and Education»)

## Prokhorov I.## The numerical solution of the Cauchy problem for the radiative transfer equation with generalized matching conditions
Development and construction of the approximate solution methods for the unsteady transport equations is an urgent problem in the study of various mathematical models of physical processes. These are models of the atmospheric optics and propagation of gamma rays in matter, neutron diffusion and kinetic theory of gases, the growth population of cells and multicellular organisms.
It is proved that the initial-value problem for the unsteady transport equation in an inhomogeneous plane layer with generalized matching conditions on the interfaces has the unique solution. It is shown that for continuous initial and boundary data and associated restrictions on the interface operator the solution of the Cauchy problem is continuous in the domain of the continuity of coefficients. For the Fresnel conditions on the interface on the basis of the Monte Carlo method the algorithm for solving the problem is proposed.
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