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| Ascher U., Petzold L. — Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations |
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| Предметный указатель |
Mode, solution of 30 167
Model reduction 98
Molecular Dynamics 114
Moving mesh method (PDEs) 254
Multiple shooting method 182
Multiple shooting method on parallel processors 184
Multiple shooting method, compactification 190
Multiple shooting method, matrix 184 202
Multiple shooting method, patching conditions 183
Multiple time scales 50
Multirate method 110
Multistep codes, DASPK 153
Multistep codes, DASSL 153
Multistep codes, DIFSUB 153
Multistep codes, ODE 153
Multistep codes, VODE 153
Multistep codes, VODPK 153
Multistep methods 123
Multistep methods, absolute stability 141
Multistep methods, Adams methods 124
Multistep methods, BDF 129
Multistep methods, characteristic polynomials 134
Multistep methods, consistency 134
Multistep methods, DAE 267
Multistep methods, error constant 133
Multistep methods, implementation 143
Multistep methods, initial values 129
Multistep methods, local truncation error 132
Multistep methods, order of accuracy 132
Multistep methods, predictor-corrector 144
Multistep methods, software design 146
Multistep methods, variable step-size formulae 147
NAG 66 186
NETLIB 67 111 186 222
Newton iteration in shooting method 178
Newton iteration, backward Euler method 54
Newton iteration, DAE 266
Newton iteration, difference approximation 54
Newton iteration, implicit Runge — Kutta methods 104
Newton — Kantorovich theorem 190
Newton's method, damped 209
Newton's method, modified 145
Newton's method, quasi-Newton 179
Newton's method, review 55
Nonautonomous ODE, transformation to autonomous form 82
Off-step points (multistep methods) 152
One-step methods 73
Optimal control 15
Optimal control, adjoint variables 16
Optimal control, Hamiltonian function 16
Order notation, review 38
Order of accuracy, multistep methods 132
Order of accuracy, Runge — Kutta methods 82 85 87 102
Order of accuracy, Runge — Kutta methods for DAEs 289
Order reduction 106—107
Order reduction in BVPs 219
Order reduction, DIRK, for DAEs 271
Order reduction, Runge — Kutta methods (DAE) 269
Order selection (multistep methods) 151
Order stars 109
Ordinary differential equations (ODEs) on a manifold 247
Ordinary differential equations (ODEs) with constraints 234
Ordinary differential equations (ODEs) with invariant 247
Ordinary differential equations (ODEs), explicit 12
Ordinary differential equations (ODEs), implicit 12 72
Ordinary differential equations (ODEs), linear constant-coefficient system 26
Oscillator, harmonic 33 64
Oscillatory system 66 242 254
Parallel method Runge — Kutta 110
Parallel shooting method 184
Parameter condensation 207
Parameter estimation 17
Parasitic roots 136
Partial differential equation (PDE) 14 205 221
Path following 212
Pendulum, stiff spring 242
Perturbations, inhomogeneity 30
Perturbations, initial data 25
Preconditioning 153
Predator-prey model 6
Predictor polynomial 149
Predictor-corrector methods 144
Principal error function 94
principal root 136
Projected collocation methods 280
Projected Runge — Kutta methods 279
Projection matrix, orthogonal 170
Quadrature rules, review 76
Quasi-linearization 196—200
Quasi-linearization with midpoint method for BVPs 199
Radau collocation 100 103 117 272 290
Reduced solution 58 244
Reduced superposition 186
Reformulation, boundary value problems 173
Regularization (DAE) 262
Review, basic quadrature rules 76
Review, Kronecker product 104
Review, matrix decompositions 57
Review, matrix eigenvalues 23
Review, matrix exponential 28
Review, Newton's method 55
Review, order notation 38
Review, Taylor's theorem for a function of several variables 75
Review, the interpolating polynomial and divided differences 125
Riccati method 172 186
Root condition 138
Rough problems 61
Runge — Kutta codes, DOPRI5 111
Runge — Kutta codes, DVERK 111
Runge — Kutta codes, ODE45 (Matlab) 111
Runge — Kutta codes, RADAU5 111
Runge — Kutta codes, RKF45 111
Runge — Kutta codes, RKSUITE 111
Runge — Kutta codes, STRIDE 111
Runge — Kutta methods, absolute stability 87 102
| Runge — Kutta methods, Butcher tree theory 108
Runge — Kutta methods, DAE 268—280
Runge — Kutta methods, diagonally implicit (DIRK) 105
Runge — Kutta methods, Dormand and Prince 4(5) embedded pair 93
Runge — Kutta methods, embedded methods 91
Runge — Kutta methods, explicit 80
Runge — Kutta methods, Fehlberg 4(5) embedded pair 92
Runge — Kutta methods, fourth-order classical 78 81 86
Runge — Kutta methods, general formulation 80
Runge — Kutta methods, half-explicit, for DAEs 280
Runge — Kutta methods, historical development 108
Runge — Kutta methods, implicit 98
Runge — Kutta methods, low-order 74
Runge — Kutta methods, mono-implicit 222
Runge — Kutta methods, order barriers 108
Runge — Kutta methods, order of accuracy by Butcher trees 83
Runge — Kutta methods, order results for DAEs 289
Runge — Kutta methods, projected, for DAEs 279
Runge — Kutta methods, singly diagonally implicit (SDIRK) 105
Runge — Kutta methods, singly implicit (SIRK) 107
Semi-explicit index-1 DAE 238
Sensitivity, analysis 95 290
Sensitivity, BVPs 175
Sensitivity, parameters 95
Shooting method 177
Shooting method, algorithm description 179
Shooting method, difficulties 179
Shooting method, difficulties for nonlinear problems 182
Shooting method, multiple shooting method 182
Shooting method, simple shooting 177
Shooting method, single shooting 177
Shooting method, stability considerations 179
Similarity transformation 24 26
simple pendulum 5 12 118 241
Singly diagonally implicit (SDIRK) Runge — Kutta methods 105
Singly implicit Runge — Kutta methods (SIRK) 107
Singular perturbation problems, relation to DAEs 244
Smoothing 232
Sparse linear system 199 203
Spectral methods (PDEs) 157
Spurious solution 110
Stability constant, BVP 169 185 203
Stability constant, IVP 30
Stability, 0-stability 41 44 82 137—140 201—203
Stability, A-stability 56 103 141
Stability, absolute stability 44
Stability, algebraic stability 117
Stability, AN-stability 69
Stability, asymptotic of the constraint manifold 250
Stability, asymptotic, difference equations 136
Stability, boundary value ODE 168—171
Stability, difference equations 136
Stability, initial value DAE 244—246
Stability, initial value ODE 23—36
Stability, initial value ODE, asymptotic 25 28 30
Stability, initial value ODE, nonlinear 31
Stability, relative stability 141
Stability, resonance instability 115
Stability, root condition (multistep methods) 138
Stability, scaled stability region 112
Stability, strong stability (multistep methods) 139
Stability, weak stability (multistep methods) 139
Stabilization of the constraint (DAE) 250
Stabilization, Baumgarte 251 259
Stabilization, coordinate projection (DAE) 281 284
Stabilization, poststabilization (DAE) 281
Stabilized index-2 formulation (DAE) 259
Stabilized march method 186
Stage order 271
State space formulation (DAE) 252
Steady state 31 211
Step size 37
Step-size selection, multistep methods 151
Step-size selection, Runge — Kutta methods 90
Stiff BVPs, finite difference methods 214
Stiff decay 58 66 101 103 112 129
Stiff decay, DAE 270
Stiff decay, ODE methods for DAEs 262
Stiffly accurate 101 112
Stiffness 49
Stiffness, BVPs 172
Stiffness, definition 50
Stiffness, system eigenvalues 50
Stiffness, transient 49
Strange Attractor 155
Superposition method 186
Switching function 63
Symmetric methods 59—61
Symmetric Runge — Kutta methods 117
Symplectic map 33
Symplectic methods 109
Taylor series method 73
Taylor's theorem, several variables, review 75
Test equation 23 44
Theta method 112
Transformation decoupling, BVP 216
Transformation decoupling, DAE 264
Transformation, stretching 70
Trapezoid method 37 128
Trapezoid method, derivation 59
Trapezoid method, dynamic equivalence to midpoint method 69
Trapezoid method, explicit 78
Trapezoid method, explicit, written as Runge — Kutta 81
Upstream difference 215 226
Upwind difference 215 226
Variable step-size multistep methods, fixed leading-coefficient strategy 149
Variable step-size multistep methods, variable-coefficient strategy 147
Variational, BVP 165
Variational, equation 31 178
Vibrating spring 10 28
Waveform relaxation 110
Well-posed problem 9
Well-posed problem, continuous dependence on the data 9
Well-posed problem, existence 9
Well-posed problem, uniqueness 9
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