Aerosol　particles　have　an　important　effect　on　changing　of　climate　and　human　health,　where　aerosols　scatter　and　absorb　the　incoming　solar　radiation,　and　thus　decrease　the　precipitation　efficiency　of　warm　clouds　and　can　cause　an　indirect　radiative　forcing　associated　with　changes　in　cloud　properties.　Meanwhile,　it　has　also　been　recognized　that　the　particles　of　aerosols　in　the　sub-micrometer　size　range　can　be　inhaled　and　thus　pose　certain　health　hazards.　In　this　paper　we　analyze　the　finite　volume　method　based　on　linear　interpolation　and　Hermite　interpolation　combined　with　the　method　of　characteristics　for　the　nonlinear　aerosol　dynamic　equations　on　time　and　particle　size,　which　involve　the　advection　process,　condensation　process　and　the　nonlinear　coagulation　process.　Numerical　experiments　for　the　multiple　log-normal　aerosol　distributions　are　further　given　to　confirm　the　theoretical　results.　(C)　2019　Elsevier　B.V.　All　rights　reserved.