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Miranker W.L. — Numerical Methods for Stiff Equations and Singular Perturbation Problems
Miranker W.L. — Numerical Methods for Stiff Equations and Singular Perturbation Problems



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Название: Numerical Methods for Stiff Equations and Singular Perturbation Problems

Автор: Miranker W.L.

Язык: en

Рубрика: Математика/Численные методы/Численный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1980

Количество страниц: 203

Добавлена в каталог: 25.02.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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, $\varepsilon$-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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