The global dynamics of the neutral H, He, O, Ne, and C components in the he
liosphere plays a vital part in the interaction of the local interstellar m
edium (LISM) with the solar wind. In this paper, a particle-mesh method is
used to solve the Boltzmann equation. This method takes into account the di
rect and reverse charge-exchange processes, photoionization, and gravitatio
n forces. The results of this incompletely self-consistent simulation of th
e dynamics of atoms and ions are discussed in the present paper.