Метод логистической функции для нахождения аналитических решений нелинейных дифференциальных уравнений
https://doi.org/10.18255/1818-1015-2015-1-23-37
Аннотация
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.
Ключевые слова
логистическая функция,
нелинейная волна,
нелинейное обыкновенное дифференциальное уравнение,
тест Пенлеве,
точное решение
При поддержке: Russian Science Foundation
Об авторе
Николай Алексеевич Кудряшов
Национальный исследовательский ядерный университет МИФИ
Россия
Россия
доктор физ.-мат. наук, профессор, зав. кафедрой,
115409 Россия, г. Москва, Каширское шоссе, 31
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Рецензия
Для цитирования:
Кудряшов Н.А. Метод логистической функции для нахождения аналитических решений нелинейных дифференциальных уравнений. Моделирование и анализ информационных систем. 2015;22(1):23-37. https://doi.org/10.18255/1818-1015-2015-1-23-37
For citation:
Kudryashov N.A. Method of the Logistic Function for Finding Analytical Solutions of Nonlinear Differential Equations. Modeling and Analysis of Information Systems. 2015;22(1):23-37. https://doi.org/10.18255/1818-1015-2015-1-23-37
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