Тип публикации: статья из журнала
Год издания: 2017
Идентификатор DOI: 10.17516/1997-1397-2017-10-4-531-536
Ключевые слова: Borel transform, Cauchy problem, Laurent expansion, Newton polytope
Аннотация: In this paper we give a proof of an analog of the Kovalevskaya theorem about analytic solvability of the Cauchy problem for a linear differential equation with constant coefficients. A major role in the proof is played by the Borel transform and the Laurent expansion of the function P-1, where P is the characteristic polynomial. ThПоказать полностьюis expansion produces an efficiently computable approximation of the solution of the Cauchy problem. The method of the proof allows to consider equations not necessarily resolved with respect to the highest derivative, however it imposes additional restrictions on the right hand side. © Siberian Federal University. All rights reserved.
Журнал: Journal of Siberian Federal University - Mathematics and Physics
Выпуск журнала: Vol. 10, Is. 4
Номера страниц: 531-536
ISSN журнала: 19971397
Издатель: Siberian Federal University