Goloviznin, V. M.; Karabasov, S. A. Balancing characteristic schemes on piece-wise constant initial data. Jumping transfer. (Russian. English summary) Zbl 1129.76343 Mat. Model. 15, No. 10, 71-83 (2003). The problem of an accurate calculation of a grid value transfer on Euler nets is still one of the most important problems of the numerical hydrodynamics. The main difficulties are connected with phenomenon display on a simple linear transfer equation with constant coefficients of the form \[ \frac{\partial \varphi}{\partial t} + c \frac{\partial \varphi}{\partial x} = 0, \quad c = const >0. \tag{(1)} \] The approximation of the Eq.(1) by linear homogeneous difference schemes on regular grids the so called phase and amplitude errors are arising . It is shown that balancing characteristic approaches to construction of numerical algorithms for the hyperbolic conservation laws gives an exact solution of the simplest convection transfer problem on a set of piece-wise constant initial functions. Reviewer: Sergei Georgievich Zhuravlev (Moskva) Cited in 3 Documents MSC: 76M20 Finite difference methods applied to problems in fluid mechanics 76R50 Diffusion Keywords:hydrodynamics; diffusion-convection PDFBibTeX XMLCite \textit{V. M. Goloviznin} and \textit{S. A. Karabasov}, Mat. Model. 15, No. 10, 71--83 (2003; Zbl 1129.76343) Full Text: MNR