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Консультация № 174808
03.12.2009, 01:08
35.00 руб.
0
2
0
Здравствуйте, прошу помощи в решении задачки по численным методам.
задание такое
1) вычислить значение опр.интеграла
методом a)прямоугольниов, б)методом трапеций, с)парабол.
2)Исследовать сходимость численно определяемых значений при уменьшении шагов интегрирования.
1)Я решил первым методом, но нужна проверка
точное значение интеграла сост-т=4,437
метод прямоугольников:
я разделил отрезок на 10 частей с шагом h=(b-a)/n=0,172
по формулам Точки деления будут: f0=a; f1=a+h; f2=a+2× h, ... , fn-1=a+(n-1)× h;
тоесть я получил
f0=1
f1=1.172
f2=1.344
f3=1.516
f4=1.688
f5=1.86
f6=2.032
f7=2.204
f8=2.376
f9=2.548
далее суммирую все fsum и получаю 17,74 и затем вычесляю площадь S=0.172*17.74=3,05128
2)Погрешность расчета 4,437 - 3,05128 = 1,38572.
Для повышения точности необходимо уменьшить n или использовать бо-лее точные квадратурные формулы
правильно ли я решил?
Прошу помощи в решении по методам трапеции и парабол.
задание такое
1) вычислить значение опр.интеграла
методом a)прямоугольниов, б)методом трапеций, с)парабол.
2)Исследовать сходимость численно определяемых значений при уменьшении шагов интегрирования.
1)Я решил первым методом, но нужна проверка
точное значение интеграла сост-т=4,437
метод прямоугольников:
я разделил отрезок на 10 частей с шагом h=(b-a)/n=0,172
по формулам Точки деления будут: f0=a; f1=a+h; f2=a+2× h, ... , fn-1=a+(n-1)× h;
тоесть я получил
f0=1
f1=1.172
f2=1.344
f3=1.516
f4=1.688
f5=1.86
f6=2.032
f7=2.204
f8=2.376
f9=2.548
далее суммирую все fsum и получаю 17,74 и затем вычесляю площадь S=0.172*17.74=3,05128
2)Погрешность расчета 4,437 - 3,05128 = 1,38572.
Для повышения точности необходимо уменьшить n или использовать бо-лее точные квадратурные формулы
правильно ли я решил?
Прошу помощи в решении по методам трапеции и парабол.
Обсуждение
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