| Abstrakt: |
Abstract: In this paper the method of spherical harmonics (MSH) is investigated, which is one of effective methods of approximative solution of the transport equation. On a unified methodical basis, boundary conditions on the outside and inner boundaries for every $P_N$-approximation of MSH are formulated. These boundary conditions coincide with Vladimirov's conditions (for $N=2r+1$) and Rumjancev's conditions (for every $N$). Symmetrization of the system of stationary equations of MSH for every $P_N$-approximation with arbitrary initial data is carried out, which extends for every $P_n$- and $P_{2r+1}$-approximation the results of V. S. Vladimirov and V. V. Smelov, respectively. The complete continuity of the resolvent of the symmetrized system is proved. On this basis the symmetrized system is solved by MSH and the convergence of approximative solutions in $W^1_2(G)$ space is proved. |
