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Консультация № 188943
15.03.2016, 09:11
0.00 руб.
15.03.2016, 11:10
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Используя значение функции
в четырёх узлах 
, расположенных на равном расстоянии h и пользуясь методом неопределённых коэффициентов, построить аппроксимацию второй производной в первой точке: 
Далее последовательно берём многочлены нулевой, первой, второй и третьей степеней, подставляя в формулу выше, получим систему линейных уравнений:
У меня возникли проблемы с решением данной системы или, кажется, я не всё правильно делаю
Используя значение функции
в четырёх узлах , расположенных на равном расстоянии h и пользуясь методом неопределённых коэффициентов, построить аппроксимацию второй производной в первой точке: Далее последовательно берём многочлены нулевой, первой, второй и третьей степеней, подставляя в формулу выше, получим систему линейных уравнений:
У меня возникли проблемы с решением данной системы или, кажется, я не всё правильно делаю
Обсуждение
19.03.2016, 21:20
общий
19.03.2016, 21:21
Адресаты:
Как я понимаю, действительно, получается система четырёх уравнений
Об авторе:
Facta loquuntur.
Facta loquuntur.
24.03.2016, 09:20
общий
это ответ
Здравствуйте, Посетитель - 399040!
При использовании метода неопределённых коэффициентов искомое выражение для производной
второго порядка в точке 
представляется в виде линейной комбинации значений функции в узлах:
При этом полагают, что данное соотношение является точным, если заданная функция может быть представлена в виде
Тогда соотношение (1) должно выполняться, например, при
Найдём вторые производные:
Если подставим последовательно выражения (2) в формулу (1), то получим
или
Теперь нужно решить последнюю систему относительно неизвестных
Вроде бы так.
С уважением.
При использовании метода неопределённых коэффициентов искомое выражение для производной
второго порядка в точке представляется в виде линейной комбинации значений функции в узлах:При этом полагают, что данное соотношение является точным, если заданная функция может быть представлена в виде
Тогда соотношение (1) должно выполняться, например, при
Найдём вторые производные:
Если подставим последовательно выражения (2) в формулу (1), то получим
или
Теперь нужно решить последнюю систему относительно неизвестных
Вроде бы так.С уважением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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