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 English edition is one third longer than the Russian
original. Mathematical rigorousness is a basic feature of this
monograph. The reader should therefore be familiar with the theory
of partial differential equations and difference equations. Some
knowledge of group theory as applied to problems in physics,
especially the theory of Lie groups, would also be useful. The
treatment of the approximation of gas dynamic equations focuses on
the question of how to characterize the typical features of
difference equations on the basis of the related differential
approximation, which can be discussed using the fully developed
theory of partial differential equations.
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