Paper's Title:

A Method of the Study of the Cauchy Problem for~a~Singularly Perturbed Linear Inhomogeneous Differential Equation

Author(s):

E. E. Bukzhalev and A. V. Ovchinnikov

Faculty of Physics,
Moscow State University,
1 Leninskie Gory,
Moscow, 119991,
Russia
E-mail: bukzhalev@mail.ru

Russian Institute for Scientific and Technical Information of the Russian Academy of Sciences,
20 Usievicha St., Moscow, 125190,
Russia
E-mail: ovchinnikov@viniti.ru

Abstract:

We construct a sequence that converges to a solution of the Cauchy problem for a singularly perturbed linear inhomogeneous differential equation of an arbitrary order. This sequence is also an asymptotic sequence in the following sense: the deviation (in the norm of the space of continuous functions) of its nth element from the solution of the problem is proportional to the (n+1)th power of the parameter of perturbation. This sequence can be used for justification of asymptotics obtained by the method of boundary functions.

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