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Консультация № 177331
19.03.2010, 00:31
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Здравствуйте уважаемые эксперты, помогите пожалуйста решить задачу:
Методом ломаных Эйлера найти приближенное решение задачи Коши, определив четыре значения функции y(x), определяемой уравнением y'=f(x,y), при начальном условии y(x0)=y0 . Шаг h изменения аргумента x взять равным 0,1.
Все промежуточные вычисления проводить с точностью до трех знаков после запятой (если округление дает ноль, то учитывать первую значащую цифру), а ответы округлить до двух знаков после запятой.
y'=x2+y3, y(1)=1.
Методом ломаных Эйлера найти приближенное решение задачи Коши, определив четыре значения функции y(x), определяемой уравнением y'=f(x,y), при начальном условии y(x0)=y0 . Шаг h изменения аргумента x взять равным 0,1.
Все промежуточные вычисления проводить с точностью до трех знаков после запятой (если округление дает ноль, то учитывать первую значащую цифру), а ответы округлить до двух знаков после запятой.
y'=x2+y3, y(1)=1.
Обсуждение
19.03.2010, 14:28
общий
это ответ
Здравствуйте, Чаркин Иван Александрович.
Для решения задачи y'=f(x,y) y(x0)=y0 в методе Эйлера вычисления проводятся по формуле
yi+1=yi+h*f(xi,yi).
xi+1=xi+h
1 шаг:
y1=1+0,1(12+13)=1,2
x1=1+0,1=1,1
2 шаг:
y2=1,2+0,1(1,12+1,23)=1,2+0,1(1,21+1,728)=1,494
x2=1,1+0,1=1,2
3 шаг:
y3=1,494+0,1(1,22+1,4943)=1,494+0,1(1,44+3,335)=1,971
x3=1,2+0,1=1,3
4 шаг:
y4=1,971+0,1(1,32+1,9713)=1,971+0,1(1,69+7,657)=2,906
x4=1,3+0,1=1,4
Для решения задачи y'=f(x,y) y(x0)=y0 в методе Эйлера вычисления проводятся по формуле
yi+1=yi+h*f(xi,yi).
xi+1=xi+h
1 шаг:
y1=1+0,1(12+13)=1,2
x1=1+0,1=1,1
2 шаг:
y2=1,2+0,1(1,12+1,23)=1,2+0,1(1,21+1,728)=1,494
x2=1,1+0,1=1,2
3 шаг:
y3=1,494+0,1(1,22+1,4943)=1,494+0,1(1,44+3,335)=1,971
x3=1,2+0,1=1,3
4 шаг:
y4=1,971+0,1(1,32+1,9713)=1,971+0,1(1,69+7,657)=2,906
x4=1,3+0,1=1,4
Форма ответа
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