Jiang, Guang-Shan; Tadmor, Eitan Nonoscillatory central schemes for multidimensional hyperbolic conservation laws. (English) Zbl 0914.65095 SIAM J. Sci. Comput. 19, No. 6, 1892-1917 (1998). The authors construct their central scheme of predictor-corrector type for the two-dimensional system of conservation laws: \[ u_t + f(u)_x + g(u)_y = 0,\quad u(x,y,0) = u_0(x,y). \] It is proved that the scheme satisfies a maximum principle and it is genuinely multidimensional, i.e., it does not necessitate dimensional splitting. It turns out that the method is applicable to several prototype two-dimensional Euler type problems. Numerical experiments illustrate the method. Reviewer: E.Schechter (Kaiserslautern) Cited in 4 ReviewsCited in 140 Documents MSC: 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 35L65 Hyperbolic conservation laws 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs Keywords:predictor-corrector scheme; numerical experiments; hyperbolic conservation laws; multidimensional systems; central difference schemes; nonoscillatory schemes; maximum principle PDFBibTeX XMLCite \textit{G.-S. Jiang} and \textit{E. Tadmor}, SIAM J. Sci. Comput. 19, No. 6, 1892--1917 (1998; Zbl 0914.65095) Full Text: DOI