The Time-Dependent Asymptotic <i>P_N</i> Approximation for the Transport Equation

In this study a spatio-temporal approach for the solution of time-dependent Boltzmann (transport) equation is derived. Finding exact using general case generally an open problem and approximate methods are usually used. One most common spherical harmonics method (the $P_N$ approximation), when transport replaced with closed set equations moments density, some closure assumption. Unfortunately, classic yields poor results low-order $N$ in highly anisotropic problems. Specifically, tails particle's positional distribution as attained by approximation, inaccurate compared to true behavior. work we present derivation linear that even approximation superior classical approximation. This closure, based on asymptotic derivation, both space time, infinite homogeneous media. We test respect one-dimensional benchmark full Green function The convergence proposed also faster (classic or modified)