|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Petzold L. — Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations |
|
|
|
| Предметный указатель |
Milne's method (multistep method) 141
Mode, solution 27 167
Model reduction 99
Molecular Dynamics 116
Moving mesh method (PDEs) 255
Multiple shooting method 183
Multiple shooting method on parallel processors 185
Multiple shooting method, compactihcation 191
Multiple shooting method, matrix 185 202
Multiple shooting method, patching conditions 183
Multiple time scales 47
Multirate method 112
Multistep codes, DASPK 156
Multistep codes, DASSL 156
Multistep codes, DIFSUB 156
Multistep codes, ODE 156
Multistep codes, VODE 156
Multistep codes, VODPK 156
Multistep methods 125
Multistep methods, absolute stability 143
Multistep methods, Adams methods 128
Multistep methods, BDF 131
Multistep methods, characteristic polynomials 137
Multistep methods, consistency 137
Multistep methods, DAE 269
Multistep methods, error constant 136
Multistep methods, implementation 146
Multistep methods, initial values 132
Multistep methods, local truncation error 134
Multistep methods, order of accuracy 134
Multistep methods, predictor-corrector 146
Multistep methods, software design 149
Multistep methods, variable step-size formulae 150
NAG 66 187
NETLIB 66 112 187
Newton iteration in shooting method 178
Newton iteration, backward Euler method 51
Newton iteration, DAE 268
Newton iteration, difference approximation 54
Newton iteration, implicit Runge — Kutta methods 105
Newton — Kantorovich theorem 190
Newton's method, damped 210
Newton's method, modified 148
Newton's method, quasi-Newton 180
Newton's method, review 53
Nonautonomous ODE, transformation to autonomous form 83
ODE on a manifold 248
ODE with constraints 234
ODE with invariant 247 250
ODE, explicit 9
ODE, implicit 10 72
ODE, linear constant-coefficient system 22
Off-step points (multistep methods) 155
One-step methods 73
Optimal control 13
Optimal control, adjoint variables 14
Optimal control, Hamiltonian function 14
Order notation, review 36
Order of accuracy, multistep methods 134
Order of accuracy, Runge — Kutta methods 83 86 88 103
Order of accuracy, Runge — Kutta methods for DAEs 291
Order reduction 108—109
Order reduction in BVPs 220
Order reduction, DIRK, for DAEs 273
Order reduction, Runge — Kutta methods (DAE) 271
Order selection (multistep methods) 154
Order stars 110
Oscillator, harmonic 30 63
Oscillatory system 65 242 255
Parallel method, Runge — Kutta 112
Parallel shooting method 185
Parameter condensation 208
Parameter estimation 15
Parasitic roots 139
Partial differential equation (PDE) 12 206 223
Path following 212
Pendulum, stiff spring 242
Perturbations, inhomogeneity 27
Perturbations, initial data 21
Preconditioning 156
Predator-prey model 4
Predictor polynomial 152
Predictor-corrector methods 146
Principal error function 95
principal root 139
Projected collocation methods 281
Projected Runge — Kutta methods 281
Projection matrix, orthogonal 170
Quadrature rules, review 75
Quasilinearization 197—200
Quasilinearization with midpoint method for BVPs 200
Radau collocation 101 104 119 274 292
Reduced solution 57 243
Reduced superposition 186
Reformulation, boundary value problems 172
Regularization (DAE) 264
Review, basic quadrature rules 75
Review, Kronecker product 105
Review, matrix decompositions 54
Review, matrix eigenvalues 19
Review, matrix exponential 24
Review, Newton's method 52
Review, order notation 36
Review, Taylor's theorem for a function of several variables 73
Review, the interpolating polynomial and divided differences 126
Riccati method 172 186
Root condition 140
Rough problems 61
Runge — Kutta codes, DOPRI5 112
Runge — Kutta codes, DVERK 112
Runge — Kutta codes, ODE45 (Matlab) 112
Runge — Kutta codes, RADAU5 113
Runge — Kutta codes, RKF45 112
Runge — Kutta codes, RKSUITE 112
Runge — Kutta codes, STRIDE 113
| Runge — Kutta methods, absolute stability 89 104
Runge — Kutta methods, Butcher tree theory 110
Runge — Kutta methods, DAE 270—282
Runge — Kutta methods, diagonally implicit (DIRK) 106
Runge — Kutta methods, Dormand & Prince 4(5) embedded pair 94
Runge — Kutta methods, embedded methods 92
Runge — Kutta methods, explicit 81
Runge — Kutta methods, Fehlberg 4(5) embedded pair 93
Runge — Kutta methods, fourth order classical 79 82 86
Runge — Kutta methods, general formulation 81
Runge — Kutta methods, half-explicit, for DAEs 281
Runge — Kutta methods, historical development 110
Runge — Kutta methods, implicit 101
Runge — Kutta methods, low order 76
Runge — Kutta methods, mono-implicit 223
Runge — Kutta methods, order barriers 110
Runge — Kutta methods, order of accuracy by Butcher trees 84
Runge — Kutta methods, order results for DAEs 291
Runge — Kutta methods, projected, for DAEs 281
Runge — Kutta methods, singly diagonally implicit (SDIRK) 107
Runge — Kutta methods, singly implicit (SIRK) 109
Semi-explicit index-1 DAE 238
Sensitivity, analysis 96 292
Sensitivity, boundary value problems 176
Sensitivity, parameters 96
Shooting method 177
Shooting method, algorithm description 179
Shooting method, difficulties 180
Shooting method, difficulties for nonlinear problems 182
Shooting method, multiple shooting method 183
Shooting method, simple shooting 177
Shooting method, single shooting 177
Shooting method, stability considerations 180
Similarity transformation 20 24
simple pendulum 3 10 120 241
Singly diagonally implicit (SDIRK) Runge — Kutta methods 107
Singly implicit Runge — Kutta methods (SIRK) 109
Singular perturbation problems, relation to DAEs 243
Smoothing 231
Sparse linear system 199 204
Spectral methods (PDEs) 161
Spurious solution 112
Stability constant, boundary value problem 169 185 203
Stability constant, initial value problem 27
Stability, 0-stability 39 42 83 139—143 201—203
Stability, A-stability 56 104 144
Stability, absolute stability 42
Stability, algebraic stability 119
Stability, AN-stability 68
Stability, asymptotic, difference equations 139
Stability, asymptotic, of the constraint manifold 251
Stability, boundary value ODE 168—171
Stability, difference equations 138
Stability, initial value DAE 245—247
Stability, initial value ODE 19—33
Stability, initial value ODE, asymptotic 21 25 27
Stability, initial value ODE, nonlinear 28
Stability, relative stability 143
Stability, resonance instability 117
Stability, root condition (multistep methods) 140
Stability, scaled stability region 114
Stability, strong stability (multistep methods) 141
Stability, weak stability (multistep methods) 141
Stabilization of the constraint (DAE) 251
Stabilization, Baumgarte 253 260
Stabilization, coordinate projection (DAE) 283 286
Stabilization, post-stabilization (DAE) 283
Stabilized index-2 formulation (DAE) 260
Stabilized march method 186
Stage order 273
State space formulation (DAE) 253
Steady state 28 212
Step size 35
Step size selection, multistep methods 154
Step size selection, Runge — Kutta methods 91
Stiff boundary value problems, finite difference methods 215
Stiff decay 57 65 102 104 114 131
Stiff decay, DAE 272
Stiff decay, ODE methods for DAEs 264
Stiffly accurate 102 114
Stiffness 47
Stiffness, boundary value problems 171
Stiffness, definition 48
Stiffness, system eigenvalues 48
Stiffness, transient 47
Strange Attractor 158
Superposition method 186
Switching function 63
Symmetric methods 58—61
Symmetric Runge — Kutta methods 119
Symplectic map 30
Symplectic methods 111
Taylor series method 74
Taylor's theorem, several variables, review 73
Test equation 21 42
Theta method 115
Transformation, decoupling (BVP) 217
Transformation, decoupling (DAE) 267
Transformation, stretching 70
Trapezoid method 35 130
Trapezoid method, derivation 58
Trapezoid method, dynamic equivalence to midpoint method 68
Trapezoid method, explicit 78
Trapezoid method, explicit, written as Runge — Kutta 82
Upstream difference 216 227
Upwind difference 216 227
Variable step size multistep methods, fixed leading-coefficient strategy 152
Variable step size multistep methods, variable-coefficient strategy 150
Variational, boundary value problem 165
Variational, equation 28 178
Vibrating spring 9 25
Waveform relaxation 112
Well-posed problem 7
Well-posed problem, continuous dependence on the data 7
Well-posed problem, existence 7
Well-posed problem, uniqueness 7
|
|
|
| Реклама |
|
|
|
|
|
О проекте