Групповые свойства разностных уравнений
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Основная коллекция
Издательство:
Физматлит
Автор:
Дородницын В. А.
Год издания: 2001
Кол-во страниц: 236
Дополнительно
Вид издания:
Практическое пособие
Уровень образования:
Аспирантура
ISBN: 5-9221-0171-4
Артикул: 631013.01.99
В книге излагаются основы нового направления в групповом анализе, связанного с приложением групп Ли к конечно-разностным уравнениям, сеткам, разностным функционалам.
Показывается, что наличие непрерывной симметрии у разностных моделей приводит так же. как и в классическом случае инвариантности дифференциальных уравнений, к понижению порядка и интегрируемости обыкновенных разностных уравнений, к наличию инвариантных (точных) решений у уравнений в частных разностных производных, к существованию разностных законов сохранения у инвариантных вариационных задач.
Рассмотрены многочисленные примеры построения разностных моделей, в которых полностью сохранена непрерывная симметрия исходных дифференциальных уравнений.
Для специалистов в области математической физики и вычислительной математики, интересующихся вопросами качественного анализа дискретных уравнений, а также для аспирантов и студентов соответствующих специальностей.
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Дородницын В.А. Групповые свойства разностных уравнений МОСКВА ФИЗМАТЛИТ ®
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