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Здравствуйте! У меня возникли сложности с таким вопросом:
Результаты эксперимента – исследование термодинамических свойств воды и водяного пара в состоянии насыщения - представлены в табл. Рассчитать промежуточное значение давления насыщенного пара P (для нечетных вариантов) или значение удельной теплоты испарения Q (для четных вариантов) при заданном значении температуры T, используя интерполяцион- ные формулы Ньютона. Сравнить полученные результаты. Расчеты проводить с тремя разрядами.
Рассчитать промежуточное значение давления насыщенного пара P (для нечетных вариантов) или значение удельной теплоты испарения Q (для четных вариантов) при заданном значении температуры T
Вопреки Вашему сообщению в мини-форуме консультации: Цитата: Adelina
Одна
я исхожу из того, что в задании указаны две таблицы, поскольку значения аргумента в одном случае заданы с шагом, равным а во втором случае -- с шагом, равным В то же время обе известные мне интерполяционные формулы Ньютона предполагают равноотстоящие узлы интерполирования. К тому же и использованная система индексирования строк таблицы свидетельствует в пользу того, что таблиц две, а не одна.
Воспользуемся сведениями, изложенными на страницах 117 -- 125 [1].
Значение аргумента для которого нужно вычислить значение удельной теплоты испарения, находится в правой половине отрезка Поэтому воспользуемся второй интерполяционной формулой; получим
Число узловых точек максимальная степень интерполяционного полинома
Вычислим конечные разности для функции и сведём их в следующую таблицу.
Подставляя данные из таблицы в формулу (1), получим
Воспользуемся первой интерполяционной формулой; получим
При этом
Подставляя данные из таблицы в формулу (2), получим
Результаты вычислений по обеим формулам совпали: кДж/кг.
Литература 1. Гутер Р. С., Овчинский Б. В. Элементы численного анализа и математической обработки результатов опыта. -- М.: Наука, 1970. -- 432 с.
Об авторе:
Facta loquuntur.
Форма ответа
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Adelina 
а во втором случае -- с шагом, равным 
В то же время обе известные мне интерполяционные формулы Ньютона предполагают равноотстоящие узлы интерполирования. К тому же и использованная система индексирования строк таблицы свидетельствует в пользу того, что таблиц две, а не одна.
для которого нужно вычислить значение 
удельной теплоты испарения, находится в правой половине отрезка 
Поэтому воспользуемся второй интерполяционной формулой; получим
максимальная степень интерполяционного полинома 
и сведём их в следующую таблицу.
кДж/кг.