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Hairer E., Lyubich Ch., Roche M. — The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods |
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Название: The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods
Авторы: Hairer E., Lyubich Ch., Roche M.
Язык:
Рубрика: Математика/
Статус предметного указателя: Готов указатель с номерами страниц
ed2k: ed2k stats
Год издания: 1989
Количество страниц: 139
Добавлена в каталог: 15.08.2008
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Предметный указатель |
15 34 64
15 34 64
15 64
-expansion 9 10 19
A-stability 19
Amplifier 108
Asymptotic expansion for half-explicit methods 50 90
Asymptotic expansion for index 1 27
Asymptotic expansion for index 2 40
Asymptotic expansion for index 3 82
BDF methods 54 91 123
Bushy trees 64
Classical order 25
codes 123
Consistent initial values 2 99
Constrained mechanical system 5
Convergence 17 25 36 40 78 92
Differential index 13
Discharge pressure control 116
Dynamic simulation problem 116
Electrical circuit 5 108 112
Elementary differentials 56
Error, error estimation 99 122
Error, error propagation 36 Lemma 6.5
Error, local error 34 76 122
Euler method 16
Explicit Runge — Kutta methods 14 20 23
Extrapolation methods 16 50 90 123
Gauss methods 16 45
Gragg’s method 21 50
Half-explicit methods, Euler 50 90
Half-explicit methods, mid-point rule 50
Half-explicit methods, Runge — Kutta 20 48 68
Homotopy 31 72
Implicit differential equation 1
Implicit Euler method 16
Implicit Euler method, asymptotic expansion 40
Implicit function theorem 2 23 99
Index, differential index 13
Index, index of nilpotency 12
Index, index-m-tractability 13
Index, order conditions 62 68
Index, order of a tree 57
Index, perturbation index 1
Index, stage order 25
Index, subject index 138
| Invariance under transformation 4 30
Jacobian matrix 92
Lady Windermere’s Fan 36
Lagrange equations 6
Lobatto IIIA methods 16 46
Lobatto IIIB methods 16
Lobatto IIIC methods 16 48
Local error 34 76
Matrix pencil 12
Newton iterations 92
Nonlinear Gaussian elimination 4
Order of convergence for half-explicit methods 48
Order of convergence for index 1 25
Order of convergence for index 2 36 40
Order of convergence for index 3 78
Order, classical order 25
Ordinary differential equation 1 14
Pendulum 8 102 118
Perturbation index 1
Perturbations 1 33 75
Perturbed asymptotic expansion 40 82
Projection 35 77 100
Quadrature formulas 15
Radau 5 106 124
Radau IA methods 16 47
Radau IIA methods 16 47
Ring modulator 112
Rosenbrock methods 29 54 123
Runge — Kutta methods 14
Runge — Kutta solution, existence 31 72
Runge — Kutta solution, uniqueness 31 72
Scaling of error estimates 102 104
Scaling of linear systems 97
Simplified Newton iterations 92
Simplifying assumptions 15 64
Singly diagonally implicit RK 16 48
Singularly perturbed problem 9 10 19
Stability function 19 25
Stage order 25
Stiff pendulum 10 119
Stiff problem 10
Transformation of systems 3 4 5
Trapezoidal rule 14 16
Trees (rooted) 56
Two phase plug flow problem 106
Two transistor amplifier 108
van der Pol equation 121
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