На правах рукописи

Елисеева Юлия Витальевна

МЕТОД СРАВНИТЕЛЬНОГО ИНДЕКСА ПРИ МАТЕМАТИЧЕСКОМ

МОДЕЛИРОВАНИИ КОЛЕБАНИЙ ДИСКРЕТНЫХ ЛИНЕЙНЫХ

СИМПЛЕКТИЧЕСКИХ СИСТЕМ

Специальность 05.13.18 - «Математическое моделирование, численные

методы и комплексы программ»

АВТОРЕФЕРАТ

Москва - 2012 г.

Работа выполнена в ФГБОУ ВПО Московском Государственном Технологическом Университете «СТАНКИН».

Научный консультант: доктор физико-математических наук, профессор Уварова Людмила Александровна

Официальные оппоненты: заслуженный деятель науки Российской Федерации, доктор физико-математических наук, профессор Латышев Анатолий Васильевич доктор физико-математических наук, профессор Кожухов Игорь Борисович доктор физико-математических наук, профессор Кипнис Михаил Мордкович Ведущее предприятие: Факультет Вычислительной Математики и Кибернетики ФГБОУ ВПО Московского Государственного Университета им. М.В. Ломоносова

Защита состоится « 29 » мая 2012 г. в 14.00 часов на заседании диссертационного совета Д 212.142.03 при ФГБОУ ВПО Московском государственном технологическом университете «СТАНКИН» по адресу:

127055, Москва, Вадковский переулок, д. 3а.

С диссертацией можно ознакомиться в библиотеке ФГБОУ ВПО Московского Государственного Технологического Университета «СТАНКИН».

Автореферат разослан « 10 » апреля 2012 г.

Ученый секретарь диссертационного совета Д 212.142.03 Семячкова Е.

. ,., ,  , .,. ., ,, [ ] Ai Bi Yi+1 = Wi Yi, i = 0, 1,...,, N, Wi =, (1) Ci D i 2n 2n :

[ ] 0I WiT JWi = J, J =, i = 0,..., N.

I (1)  :,  2n, n N,  Sturm C. M
moire sur une classe d'Equations di
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(3):

3. µk (Z[0 I]T, Z[0 I]T ) = µ (Z 1 [0 I]T, Z 1 Z[0 I]T ), k = 1, 2.

4. µ2 (Z[0 I]T, Z[0 I]T ) = µ (Z[0 I]T, Z[0 I]T ), 7. 0 µ(Y, Y ) min(rangw, rangX), w µ(W Z[0 I]T, W Z[0 I]T ) = µ(Z[0 I]T, Z[0 I]T ) + µ(W Z[0 I]T, W [0 I]T ) (12), 3. µ(W, W ) = rang(B) rang(B) + µ (W, W ) µ(W Z[0 I]T, W Z[0 I]T ) = µ(Z[0 I]T, Z[0 I]T ) + µ(W Z[0 I]T, W [0 I]T ) (1).

10 ().

11 ().

, Yi = Zi [0, I]T, Yi = Zi [0, I]T.

() (17),(19).

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(23), ZN +1 (b)[0 I] = Z0 (a)[0 I] = [0 I].

#(Z (a), Z p = l (Y R0 R0 = R0 R0 T, RN +1 RN +1 = RN +1 RNT, rang[R0 R0 ] = rang[RN +1 RN +1 ] N0 [0, N + 1].

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10 1.280672477702526e-004 2.242991865505127e- 103 1.280810673797161e-006 2.242029906268870e- 104 1.280812403183678e-008 5.326204188804695e- (35) Qj(i) = Uj(i) X Ci Qj(i+1) Ai + Di Qj(i) Qj(i+1) Bi Qj(i) = 0, Wi = NT [Vi ], (38).

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