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Эта публикация цитируется в 3 научных статьях (всего в 3 статьях)
On some numerical integration curves for PDE in neighborhood of "butterfly" catastrophe point
Oleg Yu. Khachay, Pavel A. Nosov Ural Federal University, Ekaterinburg, Russia
Аннотация:
We consider a three-dimensional nonlinear wave equation with the source term smoothly changing over time and space due to a small parameter. The behavior of solutions of this PDE near the typical "butterfly" catastrophe point is studied. In the framework of matched asymptotic expansions method we derive a nonlinear ODE of the second order depending on three parameters to search for the special solution describing the rapid restructuring of the solution of the PDE in a small neighborhood of the catastrophe point, matching with expansion in a more outer layer. Numerical integration curves of the equation for the leading term of the inner asymptotic expansion are obtained.
Ключевые слова:
Matched asymptotic expansions, Numerical integration, Butterfly catastrophe, Nonlinear ODE and PDE.
Образец цитирования:
Oleg Yu. Khachay, Pavel A. Nosov, “On some numerical integration curves for PDE in neighborhood of "butterfly" catastrophe point”, Ural Math. J., 2:2 (2016), 127–140
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/umj26 https://www.mathnet.ru/rus/umj/v2/i2/p127
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Страница аннотации: | 174 | PDF полного текста: | 58 | Список литературы: | 39 |
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