Monograph / Samara A. A. , Koldoba A. In. , Poveschenko Yu. A. , Tishkin V. F. , Favorsky A. P. - Minsk: Kriteriy CJSC, 1996. - 276 s. , OCR. (Institute of Mathematical Modeling RAS). The monograph is devoted to the development and study of difference schemes on irregular grids, on the topological and geometric structure of which minimal reasonable restrictions are imposed. Difference schemes of the method of reference operators for elliptic equations and variational-difference schemes for Lagrangian gas dynamics equations in two-dimensional (usually flat) geometry are considered .. These approaches allow us to approximate the equations of mathematical physics, written in terms of invariant operators of the first order div, grad, rot and their combinations. The main attention is paid to the development of a mathematical apparatus for the study of difference schemes, not based on any assumptions about the structure of the calculation grid. Issues of software implementation of the corresponding computational algorithms with dynamic organization of computer memory are considered.