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| Авторизация |
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| Miranker W.L. — Numerical Methods for Stiff Equations and Singular Perturbation Problems |
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| Предметный указатель |
Accuracy, degree of 92
Accuracy, higher 48
Accuracy, order p 3
AD 125—129
Ad, range of 128 133
Adams 16
Adams, Bashforth 16
Adams, Moulton 16
Adjoint representation 125
Algorithm 35 36 183
Algorithm, refinement of 122
Aliasing 70—73
Aliasing, example of 71 72
Amplification, factor 2 57
Amplification, operator 2 74
applications 7—13 28 107 173—175
Approximate solution 15
Asymptotic 165
Asymptotic analysis 9
Asymptotic analysis, expansion 89 105
Asymptotic analysis, expansion, growth condition for 115
Asymptotic analysis, expansion, matched 106
Asymptotic analysis, form 109
Asymptotic analysis, scale 113
Average problem 134
Average procedure 142 169
Average process 134
Average(ing) 115 126 137 142 150 154 161 162 168
Average, accelerated computation of 138
Average, algebraic characterization of 125
Average, Bogoliubov method of 113
Average, existence of 116 117
Average, functional 149
Backward differentiation formula 16 33 40
Balance equation, mass and heat 11
Block, decomposition 117
Block, diagonal matrix 134
Boundary layer 6 90 93 94 104
Boundary layer, behavior 89
Boundary layer, coefficients 90
Boundary layer, formalism 89
Boundary layer, numerical method 89 91 100
Boundary layer, numerical method,  -independent 95
Boundary layer, property 98
Boundary layer, terms 104
Boundary value, problem 175 188
Boundary value, problem, canonical form 175
Boundary value, problem, singularly perturbed 175
Catalytic fluidized bed 11
Central limit theorem 174
Certaine’s method 43 44 48 72
Chaotic behavior 174
Characteristic 77
Characteristic, equation 21 30
Cluster 36 38 57 68 70
Cluster, disjoint 66
Coefficient, bounded 65
Coefficient, determination of 49
Coefficient, matricial 63
Computational experiments for boundary layer method 100—103
Computational experiments for finite equations 40—42
Computational experiments for method of averaging 160
Computational experiments for partial differential equations 83—87
Computational experiments for turning point problems 187—193
Computational experiments for two-time method 123—124
Computational experiments for, extrapolation method for highly oscillatory problem 141—148
Computational experiments for, extrapolation method for rapidly equilibrating problem 105—108
Condition number 34
Conjugate gradient, method 35—42
Conjugate gradient, steps 39 42
Connection theory 175
Consistency, constraints 77 78 80
Consistency, relations 74
Consistent 17
Consistent, formulas 77 78
Consistent, formulas, fitted at high frequency 78
Convergence, quadratic 34
Convergence, theorem 18 156
Convergent method 18
Convex hull 165
Correction 44
Courant number 87
Criterion, convergence 138
Criterion, numerical 122
Data, discontinuous 75 82
Data, Hermite interpolatory 45
Data, highly oscillatory 76
Data, low frequency 87
Difference, divided, backward 183
Difference, divided, directional 184
Difference, divided, forward 183
Difference, equation, linear 21
Difference, equation, singularly perturbed 164
Difference, scheme 68 79 81
Difference, scheme, two level 74
Diophantine approximation 139
Direction field 168
Discretization, directional 184
Eell-posed problem 14
Elimination method 35 42
Endomorphism 125
Enzyme reaction 10 107
Error, algebraic 42
Error, analysis 1 59 73
Error, analysis, local 59
Error, constant 25
Error, cumulative 18
Error, equation 62
Error, equation, solution of 63 64
Error, estimate 36 38 161
Error, global 2 18 40 42 64 74
Error, global, analysis 59 60 155
Error, global, equation 62
Error, initial 59
Error, local 66 67
Error, pointwise 75 87
Error, truncation, local 161
Euclidean norm 42 149
Euler, formula 16 28 69
Euler, formula, backward 24
Euler, method 2 3 94 124
Euler, method, forward 68
Euler, method, modified 100
Exponential fitting for 55—88 73
Exponential fitting for linear multistep method 56
Exponential fitting for matricial case 61—69
Exponential fitting for oscillatory case 69—73
Extrapolation approach 105
Extrapolation formula 105 142
Extrapolation method 103 106 107 137 140
Finite equations 15 34
Fitting 60
Fitting matricial case 61—73
Fitting minimax 58 75
Fitting oscillatory case 69—73
Fitting partial differential equations 73 8
Fitting point 57 58
Fixed point 168
Forcing terms, nonlinear 121
Fourier, coefficients 71 72
Fourier, series 71
Fourier, series, discrete 70 72
Fourier, transform 75 79 151 152
Fourier, transform, methods 139
Frequency(ies) 9 70—73
Frequency, difference of 73
Frequency, high 9 78
Frequency, sum of 73
Functional 151
Functional, evaluation 149
| Functional, generalized local truncation error 162
Functional, initial 155
Functional, linear 152
Gear’s package 33 107 108
Gene pool 12 173
Group, compact 128
Group, linear transformation, nonsingular 125
Group, orthogonal 128
Group, sub- 125 128
Harmonic 28
Harmonic, motion 111
Helix 112
Hyperplane 166
Hyperplane, separating 165
Ill-conditionedl 4 34 73 75 111 112 149
Inequalities, set of 168
Initial condition 93 98
Initial value problem 1 6 73
Instability 4
Interpolation method 43
Interpolation, polynomial 44 73
Interpolation, polynomial, Hermite 45
Invariant statement 128
Invariant subspace 36 135
Invariant terminology 127 129
Irregular neighborhood 176 177 183
Irregular point 177 183 187
Isomorphism 152
Isomorphism, isometric 152
Iterative scheme 34 35
Jain’s method 44—48
Kirchoff current law 10
Lagrange multipliers 77
Limit cycle 9
Linear multistep, formula 21 150
Linear multistep, formula, stable 17 18
Linear multistep, method 13 15
Linear multistep, method, A-stable 22—29
Linear multistep, method, consistent 17
Linear multistep, method, convergent 18
Linear multistep, method, examples of 16
Linear multistep, method, explicit 15 25
Linear multistep, method, implicit 15 33
Linear multistep, method, matricial 61
Linear multistep, method, order of 17 26
Linear multistep, operator 14
Linear multistep, theory 13—18
Lipschitz, constant 14 150 161
Lipschitz, continuous 150
Matricial method 162
Matricial method, multistep 61
Matrix, diagonalizable 169 172
Matrix, diagonalizable, simultaneously 134
Matrix, exponential 44
Matrix, fundamental 119 121 122
Matrix, inertial 130
Matrix, normal 116
Matrix, skew symmetric 134
Matrix, symmetric 36 41
Matrizant 10
Maximum principle 192
Mechanical system 130
mesh 15 74
Mesh, coarse 93
Mesh, fine, calculation 93
Mesh, increment 91 154
Mesh, point 2
Mesh, point, irregular 183
Mesh, point, neighboring 183
Mesh, point, regular 183
Mesh, refinement 149
Mesh, refinement, method 192
Mesh, sub- 107
Mid-point formula 16
Minimal norm, functions of 151
Minimization problem 75 76
Minimization problem, constrained 81
Minimum principle 28
Minor function 186
Mode, nonstiff 33
Mode, quiescent 33
Mode, varying, rapidly 6 57 70 93
Mode, varying, slowly 6 57
Model problem 73 110 136 149
Moebious transformation 26
Moment, condition 76
Moment, condition, generalized 154 156 157 159 161
Moment, equations, generalized 155
Momentum vector 131
Multi-time expansion 136
Newton method 16 34 100
Noisy measurement 12
Nonlinear effect 73
Nonlinear methods 43
Norm, uniformly bounded 64
Numerical approximation 74 111
Numerical method 68
Numerical method, explicit 105
Numerical solution concept 111
Nystrom’s method 16
Oscillatory 123
Oscillatory, case 69—73
Oscillatory, data 76
Oscillatory, highly 69 70 162
Oscillatory, matrix 113 169
Oscillatory, problem, highly 112
Oscillatory, solutions 9 109
Oscillatory, solutions, highly 29 142
Oscillatory, system, highly 72
Outer solution 6 89 104
Parabolic cylinder functions 180
Parasitic effect 10
Partial differential equation 73 87
Partial differential equation, evolutionary type 73
Partial pressure 11
Partition 60
Pattern recognition 164
Periodic 70 139
Periodic function 142
Periodic function, almost 123 137 139
Periodic sequence 167
Periodic solution 9
Permanent state 34
Polynomial 44 60
Polynomial, fundamental 3
Polynomial, interpolation 45
Polynomial, minimal degree 3
Polynomial, trigonometric 73
Population genetics 12 173
Precision, degree of 14 15
Preconditioning 133 134
Prediction 38—40
Prediction, process 40
Prediction, step 40
Predictor 44
Principal function 186
Projection 128 135
Projection, operator 128
Quiescence 70
Random 41
Random variable 173
Rapid, change 69
Rapid, change region 185
Rapid, equilibrating solution 170
Rapid, motion 140
Rapid, transition 8
Recurrence(s), relation 2 11 57 166
Recurrence(s), singularly perturbed 164
Recurrence(s), system of 165
Reducible transformation, completely 128
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