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| Ïîèñê ïî óêàçàòåëÿì |
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| Golberg M.A. — Numerical Solution of Integral Equations |
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| Ïðåäìåòíûé óêàçàòåëü |
Abel integral equations, algorithm choice in computation 403—406
Abel integral equations, complications related to 375—376
Abel integral equations, data functional strategy 402—403
Abel integral equations, first-kind, in geometric probability 377
Abel integral equations, first-kind, in interferometry 377
Abel integral equations, first-kind, in stereology 378
Abel integral equations, in seismology 379—380
Abel integral equations, in tomography 380—381
Abel integral equations, numerical analysis of 382—387
Abel integral equations, original formulation of 373—374
Abel integral equations, pseudoanalytic methods 386 387—394
Abel integral equations, second-kind, in stereology 379
Abel integral equations, stabilized evaluation of inversion formulas 386—387 400—402
Abel integral equations, Weiner filtering 386 394—400
Accelerated projection methods 89—90
Affine operator 142 143
Airfoil equation see "Generalized airfoil equation"
Approximate methods, computer use and 323
Aspherical gravitational potential, in numerical method in astrodynamics 147—148
Astrodynamics see "Numerical methods in astrodynamics"
Atkinson — Bogomolny direct analysis 110
Banach contraction theorem 153
Banach space 73—74 76
Boundary element methods 11 14—21
Boundary element methods, collocation methods 19—20 21
Boundary element methods, strongly elliptical operator framework 14—15
Boundary element methods, theorems in 15—19 20—21
Boundary integral equations, boundary element methods 11 14—21
Boundary integral equations, boundary element methods, collocation methods 19—20 21
Boundary integral equations, boundary elements methods, strongly elliptical operator framework 14—15
Boundary integral equations, boundary elements methods, theorems in 15—19 20—21
Boundary integral equations, iterative methods 25—29
Boundary integral equations, iterative methods, two-grid method 26—29
Boundary integral equations, Laplace equation reformulations, direct BIE methods 4—5 7
Boundary integral equations, Laplace equation reformulations, indirect BIE methods 5—7
Boundary integral equations, Laplace equation reformulations, piecewise smooth boundaries 8—9
Boundary integral equations, Laplace equation reformulations, smooth boundary case 7—8
Boundary integral equations, numerical integration 22—25
Boundary integral equations, numerical integration, boundary element integrations 22—25
Boundary integral equations, numerical methods for 10—14
Boundary integral equations, numerical methods for, collocation methods 11
Boundary integral equations, numerical methods for, Galerkin methods 10 12 15
Boundary integral equations, numerical methods for, global methods 12—14
Boundary integral equations, numerical methods for, problems with 1
Boundary integral equations, superapproximation 37
Boundary value problem see "Planing surface problem"
Canonical function 315
Cauchy singular integral equations 72 73 89
Cauchy singular integral equations, applications of 183—184
Cauchy singular integral equations, collocation method 220—229
Cauchy singular integral equations, collocation method, continuous data 221—222
Cauchy singular integral equations, collocation method, polynomial collocation 228—229
Cauchy singular integral equations, convergence 272—296
Cauchy singular integral equations, convergence, mean square convergence of Galerkin method 273—281
Cauchy singular integral equations, convergence, of collocation method 284—287
Cauchy singular integral equations, convergence, of discrete Galerkin method 287—293
Cauchy singular integral equations, convergence, of Gaussian quadrature method 293—296
Cauchy singular integral equations, conversion to logarithmic equation 250—254
Cauchy singular integral equations, degenerate kernel methods 207—209
Cauchy singular integral equations, determining unknown constant c 190—193
Cauchy singular integral equations, determining unknown constant c, Kutta condition 191—193
Cauchy singular integral equations, direct methods 197—198
Cauchy singular integral equations, Galerkin method 209—220
Cauchy singular integral equations, generalized airfoil equation, analytical solution of 185—190
Cauchy singular integral equations, generalized airfoil equation, mapping properties of airfoil operator 198—204
Cauchy singular integral equations, generalized airfoil equation, numerical methods for 193—194
Cauchy singular integral equations, generalized airfoil equation, operator formulation 204—207
Cauchy singular integral equations, indirect methods 197—198
Cauchy singular integral equations, Kalandiya method 247—249
Cauchy singular integral equations, Kantorovich regularization 241—246
Cauchy singular integral equations, of second kind 157—168
Cauchy singular integral equations, planing surface problem in 364—365
Cauchy singular integral equations, polynomial approximation methods 258—272
Cauchy singular integral equations, polynomial approximation methods, Chawla and Kumar method 270—272
Cauchy singular integral equations, polynomial approximation methods, Cohen method 269—270
Cauchy singular integral equations, polynomial approximation methods, collocation method 263—264
Cauchy singular integral equations, polynomial approximation methods, Galerkin method 262—263
Cauchy singular integral equations, polynomial approximation methods, Gaussian quadrature method 264—266
Cauchy singular integral equations, polynomial approximation methods, Hashmi and Delves method 272
Cauchy singular integral equations, polynomial approximation methods, Lobatto quadrature 266—268
Cauchy singular integral equations, polynomial approximation methods, piecewise polynomial methods 272
Cauchy singular integral equations, polynomial approximation methods, quadrature method 264
Cauchy singular integral equations, product quadrature 246—247
Cauchy singular integral equations, quadrature methods, Gaussian quadrature method 233—236
Cauchy singular integral equations, quadrature methods, Lobatto quadrature 236—241
Cauchy singular integral equations, quadrature methods, quadrature rules for principle value integrals 230—233
Cauchy singular integral equations, Sloan iterate 283—284
Cauchy singular integral equations, superconvergence and 37
Cauchy singular integral equations, uniform convergence of Galerkin method 281—283
Cauchy — Schwarz inequality 216
Chawla and Kumar method, Cauchy singular integral equations 270—272
Chebyshev polynomial of degree 77
Chebyshev polynomials 198 199 218—219 251 257
Cohen method, Cauchy singular integral equations 269—270
Collocation method, and multidimensional problems 79
Collocation method, boundary integral equation reformulations 11 19—20 21
Collocation method, Cauchy singular integral equations 220—229 263—264
Collocation method, Cauchy singular integral equations, continuous data 221—222
Collocation method, Cauchy singular integral equations, polynomial collocation 228—229
Collocation method, convergence 284—287
Collocation method, direct analysis of discrete method 113—117
Collocation method, discrete collocation method 222
Collocation method, singular integral equations 328
Collocation method, superconvergence, collocation at Gauss points 59—63
Collocation method, superconvergence, discrete collocation method 64
Collocation method, superconvergence, for piecewise polynomials 58—59
Collocation method, superconvergence, for Volterra equations 117—120
Collocation method, superconvergence, iterated collocation method 56—63
Collocation method, superconvergence, versus iterated Galerkin method 63—64
Collocation method, zeros as collocation points 229
Compound integration rule 117
Conjugate gradient method 26
Consistency conditions 317
Convergence analysis, of projection methods 81—84
Convergence theorems and singular integral equations, collocation method 328 349—356
Convergence theorems and singular integral equations, discrete Galerkin method 356—359
Convergence theorems and singular integral equations, Galerkin method 323—328
Convergence theorems and singular integral equations, Galerkin — Petrov method 342—348
Convergence, Cauchy singular integral equations 272—296
Convergence, Cauchy singular integral equations, mean square convergence of Galerkin method 273—281
Convergence, Cauchy singular integral equations, of collocation method 284—287
Convergence, Cauchy singular integral equations, of discrete Galerkin method 287—293
Convergence, Cauchy singular integral equations, of Gaussian quadrature method 293—296
Convergence, Cauchy singular integral equations, Sloan iterate 283—284
Convergence, Cauchy singular integral equations, uniform convergence of Galerkin method 281—283
Convergence, Fromme — Goldberg rule and 224—225 227
Convergence, Gaussian quadrature method 235—236 293—296
Correction step 27
Data functional strategy, Abel integral equations 402—403
Degenerate kernel methods, Cauchy singular integral equations 207—209
Degenerate kernel operator 207
Dellwo — Friedman method, perturbed Dellwo — Friedman method 95
Direct boundary integral equations, Laplace equation reformulation 4—5 7
Dirichlet problem 4 8 19 28
Discrete collocation method 222
Discrete collocation method, superconvergence 64
Discrete Galerkin method 213 219 327
Discrete Galerkin method, convergence 287—293
Discrete Galerkin method, superconvergence 55
Discretization error 327
Earth satellite orbits, equation for 148—149
Earth satellite orbits, in numerical method in astrodynamics 148—149
Eigenvalue problem 37
Erdoes — Turan theorem 286
Fourier transform techniques 77
Frechet derivative 142 143
Frechet differentiable 141
Fredholm equation 92 96 140 143 163 166 168 198 230 241
Fredholm operator 140 319
Fromme — Goldberg quadrature rule 224—225
| Fundamental function Z 314—315
Fundamental theorem of calculus 136
Galerkin method 77—80 95—106
Galerkin method, boundary integral equation reformulations 10 12 15
Galerkin method, Cauchy singular integral equations 209—220 262—263
Galerkin method, convergence, mean square convergence 273—281
Galerkin method, convergence, of discrete Galerkin method 287—293
Galerkin method, convergence, uniform convergence 281—283
Galerkin method, direct analysis with quadrature errors 106—110
Galerkin method, discrete Galerkin method 213 219 327
Galerkin method, discrete Galerkin method, convergence of 287—293
Galerkin method, for positive-definite dominant part equations 120—126
Galerkin method, in numerical method in astrodynamics 158—161 164—165
Galerkin method, iterated Galerkin method 327 348
Galerkin method, perturbed Galerkin method 141 158—161 164—165
Galerkin method, perturbed Galerkin method, in numerical method in astrodynamics 158—161 164—165
Galerkin method, singular integral equations 323—328
Galerkin method, superconvergence 36 38—40
Galerkin method, superconvergence, discrete Galerkin method 55
Galerkin method, superconvergence, iterated Galerkin method 51—53 55
Galerkin method, superconvergence, linear functions of Galerkin approximation 48—51
Galerkin method, superconvergence, versus iterated collocation method 63—64
Galerkin — Petrov method 211—212
Galerkin — Petrov method, singular integral equations 342—348
Gauss points, collocation at 59—60
Gauss points, quadrature points 79
Gauss — Legendre quadrature rule 133
Gaussian elimination 403—404
Gaussian gravitational constant 146
Gaussian quadrature formula 24—25 37
Gaussian quadrature method, Cauchy singular integral equations 236—241 264—266
Gaussian quadrature method, convergence 235—236 293—296
Gaussian rules 231—232 263
Generalized airfoil equation, analytical solution of 185—190
Generalized airfoil equation, mapping properties of airfoil operator 198—204
Generalized airfoil equation, numerical methods for 193—194
Generalized airfoil equation, operator formulation 204—207
Geometric probability, Abel integral equations 377
Gibbs-type phenomenon 214
Global methods, boundary integral equation reformulations 12—14
Global positioning system, in numerical method in astrodynamics 149
Global positioning system, perturbative forces on 149
Global superconvergence 36
Gravitational constants, Gaussian 146
Gravitational constants, of central celestial body 146
Gravitational constants, of Newton 145
Green's function 132
Hammerstein equation 65 141 143 153
Hammerstein equation, Green's function 132
Hammerstein operator 141 144 154 157
Harmonic coefficients 148
Hashmi and Delves' method, Cauchy singular integral equations 272
Hilbert space, in numerical method in astrodynamics 138—140
HMP method, superconvergence 53—55
Hodograph technique 369
Hohmann orbit 175
Indirect boundary integral equations, Laplace equation reformulation 5—7
Inner-product space 74
Interferometry, Abel integral equations 377
Iterated collocation method, superconvergence 56—58
Iterated collocation method, superconvergence, for piecewise-polynomial spaces 58—63
Iterated collocation method, superconvergence, versus iterated Galerkin method 63—64
iterated Galerkin method 327 348
Iterated Galerkin method, superconvergence 51—53 55
Iterated Kantorovich method, superconvergence 45—48
Iterated Kantorovich regularization, as variant of projection method 88—89
Iterated projection method, superconvergence 40—45
Iterative methods, boundary integral equations 25—29
Iterative methods, two-grid methods 26—29
Jacobian of the transformation 17
Kalandiya's method, Cauchy singular integral equations 247—249
Kantorovich method, iterated method 45—48
Kantorovich method, perturbed method 93—94
Kantorovich regularization 45
Kantorovich regularization, as variant of projection method 87—88
Kantorovich regularization, Cauchy singular integral equations 241—246
Kantorovich regularization, iterated regularization 88—89
Kantorovich theorem 153 157
Keplerian motion, in numerical method in astrodynamics 147 155—156
Keplerian motion, Lambert's problem and 147
Keplerian motion, perturbed Keplerian motion 155—156
Keplerian motion, two-body problem 147
Khevedelidze theorem 317
Kutta condition 191—193 195 252 366
L-invertible coordinate system 389 394
Lagrangian interpolation polynomial of degree 352 355
Lambert problem 147 156
Laplace equation reformulations, integral equation reformulations, direct BIE methods 4—5
Laplace equation reformulations, integral equation reformulations, indirect BIE methods 5—7
Laplace equation reformulations, integral equation reformulations, piecewise smooth boundaries 8—9
Laplace equation reformulations, integral equation reformulations, Poisson equation 9
Laplace equation reformulations, integral equation reformulations, smooth boundary case 7—8
Legendre polynomials 77
Legendre polynomials in numerical method in astrodynamics 136—138
Leibnitz formula 135
Lifting line theory 370
Linear functions of Galerkin approximation, superconvergence 48—51
Lobatto quadrature, Cauchy singular integral equations 266—268
Lobatto rules 117
Mean square convergence, Galerkin's method 273—281
Mean square convergence, Galerkin's method,  278—281
Mean square convergence, Galerkin's method, direct method 276—278
Mean square convergence, Galerkin's method, indirect method 273—276
Motion, equations of, astronomical units in 146
Motion, equations of, earth satellite orbits 148—149
Motion, equations of, Gaussian gravitational constant 146
Motion, equations of, gravitational constant of the central celestial body 146
Motion, equations of, in geocentric coordinate system 145
Motion, equations of, in heliocentric coordinate system 145
Motion, equations of, Keplerian motion 147
Motion, equations of, Newton universal gravitational constant in 145
Motion, equations of, perturbative forces on global positioning system 149
Multidimensional problems, collocation methods as preference in 79
Neumann problem 4 25
Neumann — Kelvin boundary value problem 363—364
Newton universal gravitational constant 145
Newton — Kantorovich method, astrodynamics numerical technique 133 141—144
Newton — Kantorovich method, iteration 157 165—167
Noether operators 319
Nonlinear integral equations, superconvergence 64—66
Numerical method in astrodynamics see also "Motion equations
Numerical method in astrodynamics, equation of motion 144—149
Numerical method in astrodynamics, Green's function 132
Numerical method in astrodynamics, mathematical preliminaries 134—135
Numerical method in astrodynamics, mathematical preliminaries, Hilbert space 138—140
Numerical method in astrodynamics, mathematical preliminaries, integral equation and 135—136
Numerical method in astrodynamics, mathematical preliminaries, Legendre equation and 136—138
Numerical method in astrodynamics, mathematical preliminaries, Newton — Kantorovich method 141—144
Numerical method in astrodynamics, mathematical preliminaries, operator equations 140—141
Numerical method in astrodynamics, numerical examples, Earth-Mars trajectories 174—177
Numerical method in astrodynamics, numerical examples, trajectory optimization 177—178
Numerical method in astrodynamics, parallel algorithms 165—174
Numerical method in astrodynamics, parallel algorithms, constant vector setup in 168—169
Numerical method in astrodynamics, parallel algorithms, Legendre polynomial expansion 171—172 173
Numerical method in astrodynamics, parallel algorithms, matrix setups in 167—168
Numerical method in astrodynamics, parallel algorithms, solution of linear system 170—171
Numerical method in astrodynamics, perturbed Galerkin method 158—161 164—165
Numerical method in astrodynamics, perturbed Galerkin method, analytic principle in 163—164
Numerical method in astrodynamics, perturbed Galerkin method, convergence result 164—165
Numerical method in astrodynamics, perturbed Galerkin method, equivalence in 161—163
Numerical method in astrodynamics, well-posedness issue 149—150
Numerical method in astrodynamics, well-posedness issue, method of patched conics 151—152
Numerical method in astrodynamics, well-posedness issue, Newton — Kantorovich iteration 157 165—167
Numerical method in astrodynamics, well-posedness issue, perturbed Keplerian motion 155—156
Numerical method in astrodynamics, well-posedness issue, Picard iteration 154—155
Numerical method in astrodynamics, well-posedness issue, Voyager II example 152—153
Nystroem method 77 110 131 133 158 161 162—163 165
Panel method 21
Parallel processing 150 see
Parseval theorem 312—313 343
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