Carrillo, J. A.; Vecil, F. Nonoscillatory interpolation methods applied to Vlasov-based models. (English) Zbl 1151.35397 SIAM J. Sci. Comput. 29, No. 3, 1179-1206 (2007). The authors propose a general family of methods based on essentially nonoscillatory interpolations for solving transport phases of Vlasov-like systems. The dimension splitting is used to reduce transport phases to 1D coupled with the interpolation. A number of theorems and lemmas are developed for theoretical foundation. Finally experiments are performed for validation. Reviewer: Prabhat Kumar Mahanti (Saint John) Cited in 1 ReviewCited in 48 Documents MSC: 35L60 First-order nonlinear hyperbolic equations 35L45 Initial value problems for first-order hyperbolic systems 35A35 Theoretical approximation in context of PDEs Keywords:kinetic equation; flux balance method; collision model; dimension splitting Software:Vador; WENO PDFBibTeX XMLCite \textit{J. A. Carrillo} and \textit{F. Vecil}, SIAM J. Sci. Comput. 29, No. 3, 1179--1206 (2007; Zbl 1151.35397) Full Text: DOI