ABOUT SINGLE OPERATOR METHOD OF SOLUTION OF A SINGULARLY PERTURBED CAUCHY PROBLEM FOR AN ORDINARY DIFFERENTIAL EQUATION – ORDER
Ключевые слова:
Singular value perturbation, spectral decomposition, deviating argument, residual term estimation, self - adjoint operator, Gilbert-Schmidt theorem, completely continuous operator, Friedrich’s Lemma, Cauchy problem, asymptotic expansion, small parameter.Аннотация
In this paper, by the method of the deviating argument, we obtain an asymptotic expansion
of the solution of the Cauchy problem for an ordinary differential equation of ݊ െ th order with variable
coefficients, with an estimate of the residual term through the right side of the equation. Many papers
devoted to this topic are of an applied nature, and their estimates of the residual term are expressed in
terms of ܱ െlarge or െsmall, so they have a theoretical value rather than applied, as they claim. The
main advantage of the proposed method is the simplicity of its algorithm, and the residual term formula,
explicitly expressed through the right side of the equation, and its evaluation.
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Опубликован
2019-04-10
Как цитировать
Shaldanbayev A. Sh., Akylbaev M. I., Orazov I., & Beysebayeva A. (2019). ABOUT SINGLE OPERATOR METHOD OF SOLUTION OF A SINGULARLY PERTURBED CAUCHY PROBLEM FOR AN ORDINARY DIFFERENTIAL EQUATION – ORDER . Известия НАН РК. Серия физико-математическая, (2), 17–36. извлечено от https://journals.nauka-nanrk.kz/physics-mathematics/article/view/1169
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