The properties of difference schemes on oblique stencils for the hyperbolic equations

In this paper, we study various difference schemes on oblique stencils, i.e., the schemes using different space grids on different time levels. Such schemes can be useful when solving boundary value problems with moving boundaries and when using the regular grids of a non-standard structure (for example, triangular or cellular) and, also, when applying the adaptive methods.
To study the stability, we use the analysis of First Differential Approximation of finite difference schemes and the dispersion analysis. We study the meaning of the stability conditions as constraints on the geometric location of stencil elements with respect to the characteristics of the equation. In addition, we compare our results with the geometric interpretation of the stability of classical schemes. The paper also presents the generalization of oblique schemes in the case of the quasi-linear equation of transport and numerical experiments for these schemes.