Abstract
When finding solutions of differential equations it is necessary to take into account the
theorems on innovation and unity of solutions of equations. In case of non-fulfillment of the
conditions of these theorems, the methods of finding solutions of the studied equations used in
computational mathematics may give erroneous results. It should also be borne in mind that
the Cauchy problem for differential equations may have no solutions or have an infinite number
of solutions.
The author presents two statements obtained by the author about the denseness of sets
of the Cauchy problem without solutions (in the case of infinite-dimensional Banach space)
and with many solutions (in the case of an arbitrary Banach space) in the set of all Cauchy
problems.
Using two examples of the Cauchy problem for differential equations, the imperfection of
some methods of computational mathematics for finding solutions of the studied equations is
shown.
Publisher
Yuriy Fedkovych Chernivtsi National University
Subject
Computer Science Applications,History,Education
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