I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2006, VOLUME 12, NUMBER 1, PAGES 205-236
Approximation of solutions of the Monge--Ampère equations by surfaces
reduced to developable surfaces
L. B. Pereyaslavskaya
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We consider an approximate construction of the
being the graph of a -smooth
solution of the parabolic
of a special form with the initial conditions
In the method proposed, the desired solution is approximated by
a sequence of -smooth
surfaces each of
which consists of parts of surfaces reduced to developable surfaces.
In this case, the projections of characteristics of the
being curved lines in general are approximated by characteristic
projections of the surfaces being
polygonal lines composed of links.
The results of these constructions are formulated in the theorem.
Sufficient conditions for the convergence of the family of
surfaces to the
as are presented; this
allows one to construct a numerical solution of the problem with
any accuracy given in advance.
Last modified: July 8, 2006