This book is concerned with the solution of parabolic partial
differential equations by the method of nets (otherwise known
as the method of finite differences). The book is in two parts,
the first of which is devoted to the construction of net equations,
paying particular attention to the stability and the accuracy of
the approximating net equations, and the second part to the
solution of such equations. Together with classical net methods,
this book contains many recent developments due to the author
and his colleagues, which have not previously been published
in the West.
The book can profitably be read by scientists and engineers
without specialized mathematical knowledge, but is of most
value to numerical analysts. Most of the methods described
demand electronic computation, but some of the novel methods
are suitable for hand computation.
The translator has in a few instances added, in a footnote,
a clarification of the original text.
I wish to thank Mr. E. L. Albasiny of the National Physical
Laboratory for checking the accuracy of the translation and
for many helpful suggestions concerning the style. Our grateful
thanks are also due to the author for providing a list of corrections
to the Russian text.