Geodesic
On the approximate solution of the multi-group time-dependent transport equation by $P_L$-method
Applications of Mathematics, Tome 24 (1979) no. 2, pp. 133-154
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This paper concerns $l$-velocity model of the general linear time-dependent transport equation. The assumed probability of the collision (scattering, fission) depends only on the angle of the directions of the moving neutron before and after the collision. The weak formulation of the problem is given and a priori estimates are obtained. The construction of an approximate problem by $\text {P_L}$-method is given. In the symmetric hyperbolic system obtained by $\text {P_L}$-method dissipativity and $\Cal A$-orthogonality of the relevant boundary spaces are proved and the connection with the mono-velocity model of the transport equation studied in papers by U.M. Sultangazin and S.K. Godunov is shown. The work is concluded by the proof of the weak convergence of the $\text {P_L}$-method.
This paper concerns $l$-velocity model of the general linear time-dependent transport equation. The assumed probability of the collision (scattering, fission) depends only on the angle of the directions of the moving neutron before and after the collision. The weak formulation of the problem is given and a priori estimates are obtained. The construction of an approximate problem by $\text {P_L}$-method is given. In the symmetric hyperbolic system obtained by $\text {P_L}$-method dissipativity and $\Cal A$-orthogonality of the relevant boundary spaces are proved and the connection with the mono-velocity model of the transport equation studied in papers by U.M. Sultangazin and S.K. Godunov is shown. The work is concluded by the proof of the weak convergence of the $\text {P_L}$-method.
DOI : 10.21136/AM.1979.103789
Classification : 45K05, 45L05, 82A77, 82C70
Keywords: spherical-harmonics method; neutron transport equation; approximation of solution 
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Míka, Stanislav. On the approximate solution of the multi-group time-dependent transport equation by $P_L$-method. Applications of Mathematics, Tome 24 (1979) no. 2, pp. 133-154. doi: 10.21136/AM.1979.103789

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