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A Finite Element Procedure of the Second Order of Accuracy /M. Zlámal // Numer. Math. 14, 1970. P. 394–402.119Приложение AДля полноты доказательства теоремы 3 в настоящем приложении приводитсяполный список систем линейных уравнений с указанием их несовместности. Воизбежание ошибок, проверка несовместности систем была произведена в компьютерной системе для работы с символьными и численными выражениямиMaxima [77] двумя способами.

Первый способ заключался с явном составлениисистем уравнений и вызове для каждой из них метода solve(), встроенногов среду. После исключения линейно-зависимых уравнений, система Maxima произвела вычисление множества решений, которое для каждой системы оказалосьпустым. Для контроля, тот же результат был получен вторым способом, а именно, для каждой системы линейных уравнений был произведен расчет ранговосновной и расширенной матриц. Далее приведены расширенные матрицы, которые были использованы во втором способе проверки.

Ранг каждой из приведенной далее матриц равен 11, а ранги соответствующих основных матрицравны 10, что и доказывает несовместность систем уравнений. −k1 1 0 0 0 0 0 0 0 −k2 0 1 0 0 0 0 0 0 0 −k1 0 0 0 0 0 0 1 1 −k2 0 0 0 0 0 0 0 1 0 −k 0 0 0 0 0 01 0 0 −k2 0 0 0 0 0 1 0 0 0 −k 0 0 1 0 01 0 0 0 −k2 1 0 0 0 0 0 0 0 1 −k 0 0 0 01 0 0 0 0 −k2 0 0 1 0 0 0 0 0 0 −k 0 0 01 0 0 0 0 0 −k2 0 0 0 0 0 0 0 0 −1 1 1 00 0 0 0 0 1 0 0 0000000000011000000000000000000000000000001 −k1 1 0 0 0 0 0 0 0 −k2 0 0 0 0 0 0 0 1 0 −k1 0 0 0 0 0 0 1 0 −k2 1 0 0 0 0 0 0 1 0 −k 0 0 0 0 0 01 1 0 −k2 0 0 0 0 0 0 0 0 0 −k 0 0 1 0 01 0 0 0 −k2 0 0 0 1 0 0 0 0 1 −k 0 0 0 01 0 0 0 0 −k2 0 0 0 0 0 0 0 0 0 −k 0 0 01 0 0 0 0 1 −k2 0 0 0 0 0 0 0 0 −1 1 1 00 0 0 0 0 1 0 0 0000000000110000000000000000000000000000001 −k1 1 0 0 0 0 0 0 0 −k2 0 0 0 1 0 0 0 0 0 −k1 0 0 0 0 0 0 1 1 −k2 0 0 0 0 0 0 0 1 0 −k 0 0 0 0 0 01 0 0 −k2 0 0 0 0 0 0 0 0 0 −k 0 0 1 0 01 0 0 1 −k2 0 0 0 0 0 0 0 0 1 −k 0 0 0 01 0 0 0 0 −k2 0 0 1 0 0 0 0 0 0 −k 0 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0 0 0 0 01 0 0 −k2 0 0 0 0 0 0 0 1 0 −k 0 0 0 0 01 0 0 1 −k2 0 0 0 0 0 0 0 0 1 −k 0 0 0 01 0 0 0 0 −k2 0 0 1 0 1 0 0 0 0 −k 0 0 01 0 0 0 0 0 −k2 0 0 1 0 0 0 0 0 −1 1 1 00 0 0 0 0 1 0 0 0000011000000000000000000000000000000000001 −k1 0 0 0 0 0 1 0 0 −k2 0 0 0 1 0 0 0 0 0 −k1 0 0 0 0 0 0 1 0 −k2 0 0 0 0 0 0 0 0 0 −k 0 0 0 0 0 01 1 0 −k2 0 0 0 0 0 0 0 1 0 −k 0 0 0 0 01 0 0 0 −k2 0 0 0 1 0 0 0 0 1 −k 0 0 0 01 0 0 1 0 −k2 0 0 0 0 1 0 0 0 0 −k 0 0 01 0 0 0 0 0 −k2 0 0 1 0 0 0 0 0 −1 1 1 00 0 0 0 0 1 0 0 0000110000000000000000000000000000000000001 −k1 0 0 0 0 0 1 0 0 −k2 0 0 0 0 0 0 0 0 0 −k1 0 0 0 0 0 0 1 1 −k2 0 0 0 0 0 0 0 0 0 −k 0 0 0 0 0 01 0 0 −k2 0 1 0 0 0 0 0 1 0 −k 0 0 0 0 01 0 0 0 −k2 0 0 0 0 1 0 0 0 1 −k 0 0 0 01 0 0 0 0 −k2 0 0 1 0 1 0 0 0 0 −k 0 0 01 0 0 1 0 0 −k2 0 0 0 0 0 0 0 0 −1 1 1 00 0 0 0 0 1 0 0 0010010000000000000000000000000000000000001 −k1 0 0 0 0 0 1 0 0 −k2 0 0 0 0 0 0 0 0 0 −k1 0 0 0 0 0 0 1 0 −k2 0 0 1 0 0 0 0 0 0 −k 0 0 0 0 0 01 1 0 −k2 0 0 0 0 0 0 0 1 0 −k 0 0 0 0 01 0 0 0 −k2 0 0 0 1 0 0 0 0 1 −k 0 0 0 01 0 0 0 0 −k2 0 0 0 1 1 0 0 0 0 −k 0 0 01 0 0 1 0 0 −k2 0 0 0 0 0 0 0 0 −1 1 1 00 0 0 0 0 1 0 0 0010010000000000000000000000000000000000001143 −k1 0 0 0 0 0 1 0 0 −k2 0 1 0 0 0 0 0 0 0 −k1 0 0 0 0 0 0 1 0 −k2 0 0 1 0 0 0 0 0 0 −k 0 0 0 0 0 01 0 0 −k2 0 0 0 0 1 0 0 1 0 −k 0 0 0 0 01 1 0 0 −k2 0 0 0 0 0 0 0 0 1 −k 0 0 0 01 0 0 0 0 −k2 0 0 0 1 1 0 0 0 0 −k 0 0 01 0 0 0 0 0 −k2 0 0 0 0 0 0 0 0 −1 1 1 00 0 0 0 0 1 0 0 0000010000001000000000000000000000000000001 −k1 0 0 0 0 0 1 0 0 −k2 0 1 0 0 0 0 0 0 0 −k1 0 0 0 0 0 0 1 0 −k2 0 0 0 0 0 1 0 0 0 −k 0 0 0 0 0 01 0 0 −k2 0 1 0 0 0 0 0 1 0 −k 0 0 0 0 01 0 0 0 −k2 0 0 0 0 1 0 0 0 1 −k 0 0 0 01 1 0 0 0 −k2 0 0 0 0 1 0 0 0 0 −k 0 0 01 0 0 0 0 0 −k2 0 0 0 0 0 0 0 0 −1 1 1 00 0 0 0 0 1 0 0 0000010000001000000000000000000000000000001 −k1 0 0 0 0 0 1 0 0 −k2 0 0 0 1 0 0 0 0 0 −k1 0 0 0 0 0 0 1 0 −k2 1 0 0 0 0 0 0 0 0 −k 0 0 0 0 0 01 0 0 −k2 0 0 0 0 1 0 0 1 0 −k 0 0 0 0 01 1 0 0 −k2 0 0 0 0 0 0 0 0 1 −k 0 0 0 01 0 0 0 0 −k2 0 0 0 0 1 0 0 0 0 −k 0 0 01 0 0 0 0 0 −k2 0 0 1 0 0 0 0 0 −1 1 1 00 0 0 0 0 1 0 0 0000010000100000000000000000000000000000001 −k1 0 0 0 0 0 1 0 0 −k2 0 0 0 0 0 0 1 0 0 −k1 0 0 0 0 0 0 1 0 −k2 1 0 0 0 0 0 0 0 0 −k 0 0 0 0 0 01 0 0 −k2 0 1 0 0 0 0 0 1 0 −k 0 0 0 0 01 0 0 0 −k2 0 0 0 0 1 0 0 0 1 −k 0 0 0 01 0 0 0 0 −k2 0 0 0 0 1 0 0 0 0 −k 0 0 01 1 0 0 0 0 −k2 0 0 0 0 0 0 0 0 −1 1 1 00 0 0 0 0 1 0 0 0000010000100000000000000000000000000000001 −k1 0 0 0 0 0 1 0 0 −k2 0 0 0 0 0 0 0 1 0 −k1 0 0 0 0 0 0 1 0 −k2 0 0 0 0 0 0 0 0 0 −k 0 0 0 0 0 01 0 0 −k2 0 0 0 0 1 0 0 1 0 −k 0 0 0 0 01 1 0 0 −k2 0 0 0 0 0 0 0 0 1 −k 0 0 0 01 0 0 1 0 −k2 0 0 0 0 1 0 0 0 0 −k 0 0 01 0 0 0 0 1 −k2 0 0 0 0 0 0 0 0 −1 1 1 00 0 0 0 0 1 0 0 0000110000000000000000000000000000000000001 −k1 0 0 0 0 0 1 0 0 −k2 0 0 0 0 0 0 0 1 0 −k1 0 0 0 0 0 0 1 0 −k2 0 0 0 0 0 1 0 0 0 −k 0 0 0 0 0 01 0 0 −k2 0 0 0 0 0 0 0 1 0 −k 0 0 0 0 01 0 0 1 −k2 0 0 0 0 0 0 0 0 1 −k 0 0 0 01 1 0 0 0 −k2 0 0 0 0 1 0 0 0 0 −k 0 0 01 0 0 0 0 1 −k2 0 0 0 0 0 0 0 0 −1 1 1 00 0 0 0 0 1 0 0 0000011000000000000000000000000000000000001 −k1 0 0 0 0 0 1 0 0 −k2 0 0 0 0 0 0 0 0 0 −k1 0 0 0 0 0 0 1 0 −k2 0 0 0 0 0 1 0 0 0 −k 0 0 0 0 0 01 0 0 −k2 0 0 0 0 0 1 0 1 0 −k 0 0 0 0 01 0 0 0 −k2 1 0 0 0 0 0 0 0 1 −k 0 0 0 01 1 0 0 0 −k2 0 0 0 0 1 0 0 0 0 −k 0 0 01 0 0 1 0 0 −k2 0 0 0 0 0 0 0 0 −1 1 1 00 0 0 0 0 1 0 0 0010010000000000000000000000000000000000001 −k1 0 0 0 0 0 1 0 0 −k2 0 0 0 0 0 0 1 0 0 −k1 0 0 0 0 0 0 1 0 −k2 0 0 0 0 0 0 0 0 0 −k 0 0 0 0 0 01 0 0 −k2 0 0 0 0 0 1 0 1 0 −k 0 0 0 0 01 0 0 0 −k2 1 0 0 0 0 0 0 0 1 −k 0 0 0 01 0 0 1 0 −k2 0 0 0 0 1 0 0 0 0 −k 0 0 01 1 0 0 0 0 −k2 0 0 0 0 0 0 0 0 −1 1 1 00 0 0 0 0 1 0 0 0000110000000000000000000000000000000000001144Приложение БВо избежание ошибок, матрицы, перечисленные в приложении A были сгенерированы при помощи компьютерной программы.

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