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Консультация № 177774
09.04.2010, 17:21
42.70 руб.
0
1
1
Уважаемые эксперты, решите пожалуйста Ду II-го порядка:
y``+2*(y`/x)-3*y=2
с условиями:
y`(0.8)=1.5
2*y(1.1)+y`(1.1)=3
Т.е. a=0.8, b=1.1
Желательно более подробнее. Можно решить любым численным методом(стрельбы, диф. прогонки и т.д.) и ответ показать в виде сетки с значениями x, y(x) и y`(x), можно и любым другим образом, как будет удобнее. Просто решил эту задачу методом стрельбы в паскале но не знаю как проверить решение.
y``+2*(y`/x)-3*y=2
с условиями:
y`(0.8)=1.5
2*y(1.1)+y`(1.1)=3
Т.е. a=0.8, b=1.1
Желательно более подробнее. Можно решить любым численным методом(стрельбы, диф. прогонки и т.д.) и ответ показать в виде сетки с значениями x, y(x) и y`(x), можно и любым другим образом, как будет удобнее. Просто решил эту задачу методом стрельбы в паскале но не знаю как проверить решение.
Обсуждение
Неизвестный
11.04.2010, 18:06
общий
это ответ
Здравствуйте, S K A L T .
Это уравнение имеет общее решение:
y=C1*sinh([$8730$]3*x)/x+C2*cosh([$8730$]3*x)/x-2/3
учитывая краевые условия, можно найти точные значения С1 и С2, но они довольно громоздкие.
Приближенное решение:
y=1.21861*sinh([$8730$]3*x)/x-0.725935*cosh([$8730$]3*x)/x-2/3
(x;y(x);y'(x))
(0.8;0.260182;1.499992)
(0.9;0.407087;1.454032)
(1.0;0.553675;1.489231)
(1.1;0.706976;1.586011)
Графики решения: y(x) (красный) и y'(x) (зеленый)
Это уравнение имеет общее решение:
y=C1*sinh([$8730$]3*x)/x+C2*cosh([$8730$]3*x)/x-2/3
учитывая краевые условия, можно найти точные значения С1 и С2, но они довольно громоздкие.
Приближенное решение:
y=1.21861*sinh([$8730$]3*x)/x-0.725935*cosh([$8730$]3*x)/x-2/3
(x;y(x);y'(x))
(0.8;0.260182;1.499992)
(0.9;0.407087;1.454032)
(1.0;0.553675;1.489231)
(1.1;0.706976;1.586011)
Графики решения: y(x) (красный) и y'(x) (зеленый)
5
Спасибо, похоже я где то ошибся с программой
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