This book presents a new, efficient numerical-analytical method for
solving the Laplace equation on an arbitrary polygon. This method,
called the approximate block method, overcomes indicated
difficulties and has qualitatively more rapid convergence than
well-known difference and variational-difference methods. The block
method also solves the complicated problem of approximate conformal
mapping of multiply-connected polygons onto canonical domains with
no preliminary information required. The high-precision results of
calculations carried out on the computer are presented in an
abundance of tables substantiating the exponential convergence of
the block method and its strong stability concerning the
rounding-off of errors.
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