maisМоделирование и анализ информационных системModeling and Analysis of Information Systems1818-10152313-5417Yaroslavl State University10.18255/1818-1015-2015-1-23-37mais-229Research ArticleОригинальные статьиArticlesМетод логистической функции для нахождения аналитических решений нелинейных дифференциальных уравненийMethod of the Logistic Function for Finding Analytical Solutions of Nonlinear Differential EquationsКудряшовНиколай АлексеевичKudryashovN. A.

доктор физ.-мат. наук, профессор, зав. кафедрой,

 115409 Россия, г. Москва, Каширское шоссе, 31

доктор физ.-мат. наук, профессор, зав. кафедрой,

115409 Russian Federation, Moscow, Kashirskoe shosse, 31

nakudryashov@mephi.ruНациональный исследовательский ядерный университет МИФИРоссияNational Research Nuclear University MEPHIRussian Federation2015200220152212337Copyright © Кудряшов Н.А., 20152015Кудряшов Н.А.Kudryashov N.A.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.mais-journal.ru/jour/article/view/229

Для нахождения точных решений нелинейных дифференциальных уравнений используется метод логистической функции. Применение метода иллюстрируется на примере нелинейного обыкновенного дифференциального уравнения четвертого порядка. Представлены аналитические решения, полученные с помощью этого метода. Как оказалось, эти решения выражаются через экспоненциальные функции.

The method of the logistic function is presented for finding exact solutions of nonlinear differential equations. The application of the method is illustrated by using the nonlinear ordinary differential equation of the fourth order. Analytical solutions obtained by this method are presented. These solutions are expressed via exponential functions.

logistic function, nonlinear wave, nonlinear ordinary differential equation, Painlev´e test, exact solution

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The authors declare that there are no conflicts of interest present.