I am very glad that this book is now accessible to English-speaking scientists. During the
three years following the publication of the original Russian edition, the method of
differential approximation has been rapidly expanded and unfortunately I was unable to
incorporate into the English edition all of the material which whould have reflected its
present state of development. Nevertheless, a considerable amount of recently obtained
results have been added and the bibliography has been enlarged accordingly, so that the …

The method of differential approximation, a new method commonly used in the analysis of
the properties of difference schemes and approximating hyperbolic equations including
gasdynamic equations, is presented. It is shown that the differential approximation method
makes it possible to develop new difference schemes with specified properties, to analyze
the properties of the existing and newly developed difference schemes, and to classify these
schemes on the basis of various characteristics. Applications of the method to gas dynamics …