Illner, R.; Rjasanow, S. Difference scheme for the Vlasov-Manev system. (English) Zbl 0927.65127 Doc. Math. 4, 179-201 (1999). At first, the Vlasov-Manev equation is described and its properties are summarized. Then, the authors derive a finite difference scheme for the Vlasov-Manev equation in one space and one velocity dimension. Properties of this finite difference scheme are formulated and proved, e.g. the existence of the solution of the finite difference scheme, the mass conservation of this scheme, and the stability in the discrete maximum norm with respect to the initial data. Finally, some numerical experiments are presented. Reviewer: M.Jung (Chemnitz) MSC: 65N06 Finite difference methods for boundary value problems involving PDEs 65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs 85A05 Galactic and stellar dynamics 35Q72 Other PDE from mechanics (MSC2000) Keywords:Vlasov-Manev system; finite difference methods; stability; numerical examples PDFBibTeX XMLCite \textit{R. Illner} and \textit{S. Rjasanow}, Doc. Math. 4, 179--201 (1999; Zbl 0927.65127) Full Text: EuDML EMIS