Properties of Difference Schemes with Oblique Stencils for Hyperbolic Equations

In this paper, various difference schemes with oblique stencils, i.e., schemes using different space grids at different time levels, are studied. Such schemes may be useful in solving boundary value problems with moving boundaries, regular grids of a non-standard structure (for example, triangular or cellular ones), and adaptive methods. To study the stability of finite difference schemes with oblique stencils, we analyze the first differential approximation and dispersion. We study stability conditions as constraints on the geometric locations of stencil elements with respect to characteristics of the equation. We compare our results with a geometric interpretation of the stability of some classical schemes. The paper also presents generalized oblique schemes for a quasilinear equation of transport and the results of numerical experiments with these schemes.