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Golberg M.A. Ч Numerical Solution of Integral Equations
Golberg M.A. Ч Numerical Solution of Integral Equations

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Ќазвание: Numerical Solution of Integral Equations

јвтор: Golberg M.A.

язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1990

 оличество страниц: 430

ƒобавлена в каталог: 30.11.2013

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
Abel integral equations, algorithm choice in computation      403Ч406
Abel integral equations, complications related to      375Ч376
Abel integral equations, data functional strategy      402Ч403
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      379Ч380
Abel integral equations, in tomography      380Ч381
Abel integral equations, numerical analysis of      382Ч387
Abel integral equations, original formulation of      373Ч374
Abel integral equations, pseudoanalytic methods      386 387Ч394
Abel integral equations, second-kind, in stereology      379
Abel integral equations, stabilized evaluation of inversion formulas      386Ч387 400Ч402
Abel integral equations, Weiner filtering      386 394Ч400
Accelerated projection methods      89Ч90
Affine operator      142 143
Airfoil equation      see "Generalized airfoil equation"
Approximate methods, computer use and      323
Aspherical gravitational potential, in numerical method in astrodynamics      147Ч148
Astrodynamics      see "Numerical methods in astrodynamics"
Atkinson Ч Bogomolny direct analysis      110
Banach contraction theorem      153
Banach space      73Ч74 76
Boundary element methods      11 14Ч21
Boundary element methods, collocation methods      19Ч20 21
Boundary element methods, strongly elliptical operator framework      14Ч15
Boundary element methods, theorems in      15Ч19 20Ч21
Boundary integral equations, boundary element methods      11 14Ч21
Boundary integral equations, boundary element methods, collocation methods      19Ч20 21
Boundary integral equations, boundary elements methods, strongly elliptical operator framework      14Ч15
Boundary integral equations, boundary elements methods, theorems in      15Ч19 20Ч21
Boundary integral equations, iterative methods      25Ч29
Boundary integral equations, iterative methods, two-grid method      26Ч29
Boundary integral equations, Laplace equation reformulations, direct BIE methods      4Ч5 7
Boundary integral equations, Laplace equation reformulations, indirect BIE methods      5Ч7
Boundary integral equations, Laplace equation reformulations, piecewise smooth boundaries      8Ч9
Boundary integral equations, Laplace equation reformulations, smooth boundary case      7Ч8
Boundary integral equations, numerical integration      22Ч25
Boundary integral equations, numerical integration, boundary element integrations      22Ч25
Boundary integral equations, numerical methods for      10Ч14
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      12Ч14
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      183Ч184
Cauchy singular integral equations, collocation method      220Ч229
Cauchy singular integral equations, collocation method, continuous data      221Ч222
Cauchy singular integral equations, collocation method, polynomial collocation      228Ч229
Cauchy singular integral equations, convergence      272Ч296
Cauchy singular integral equations, convergence, mean square convergence of Galerkin method      273Ч281
Cauchy singular integral equations, convergence, of collocation method      284Ч287
Cauchy singular integral equations, convergence, of discrete Galerkin method      287Ч293
Cauchy singular integral equations, convergence, of Gaussian quadrature method      293Ч296
Cauchy singular integral equations, conversion to logarithmic equation      250Ч254
Cauchy singular integral equations, degenerate kernel methods      207Ч209
Cauchy singular integral equations, determining unknown constant c      190Ч193
Cauchy singular integral equations, determining unknown constant c, Kutta condition      191Ч193
Cauchy singular integral equations, direct methods      197Ч198
Cauchy singular integral equations, Galerkin method      209Ч220
Cauchy singular integral equations, generalized airfoil equation, analytical solution of      185Ч190
Cauchy singular integral equations, generalized airfoil equation, mapping properties of airfoil operator      198Ч204
Cauchy singular integral equations, generalized airfoil equation, numerical methods for      193Ч194
Cauchy singular integral equations, generalized airfoil equation, operator formulation      204Ч207
Cauchy singular integral equations, indirect methods      197Ч198
Cauchy singular integral equations, Kalandiya method      247Ч249
Cauchy singular integral equations, Kantorovich regularization      241Ч246
Cauchy singular integral equations, of second kind      157Ч168
Cauchy singular integral equations, planing surface problem in      364Ч365
Cauchy singular integral equations, polynomial approximation methods      258Ч272
Cauchy singular integral equations, polynomial approximation methods, Chawla and Kumar method      270Ч272
Cauchy singular integral equations, polynomial approximation methods, Cohen method      269Ч270
Cauchy singular integral equations, polynomial approximation methods, collocation method      263Ч264
Cauchy singular integral equations, polynomial approximation methods, Galerkin method      262Ч263
Cauchy singular integral equations, polynomial approximation methods, Gaussian quadrature method      264Ч266
Cauchy singular integral equations, polynomial approximation methods, Hashmi and Delves method      272
Cauchy singular integral equations, polynomial approximation methods, Lobatto quadrature      266Ч268
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      246Ч247
Cauchy singular integral equations, quadrature methods, Gaussian quadrature method      233Ч236
Cauchy singular integral equations, quadrature methods, Lobatto quadrature      236Ч241
Cauchy singular integral equations, quadrature methods, quadrature rules for principle value integrals      230Ч233
Cauchy singular integral equations, Sloan iterate      283Ч284
Cauchy singular integral equations, superconvergence and      37
Cauchy singular integral equations, uniform convergence of Galerkin method      281Ч283
Cauchy Ч Schwarz inequality      216
Chawla and Kumar method, Cauchy singular integral equations      270Ч272
Chebyshev polynomial of degree      77
Chebyshev polynomials      198 199 218Ч219 251 257
Cohen method, Cauchy singular integral equations      269Ч270
Collocation method, and multidimensional problems      79
Collocation method, boundary integral equation reformulations      11 19Ч20 21
Collocation method, Cauchy singular integral equations      220Ч229 263Ч264
Collocation method, Cauchy singular integral equations, continuous data      221Ч222
Collocation method, Cauchy singular integral equations, polynomial collocation      228Ч229
Collocation method, convergence      284Ч287
Collocation method, direct analysis of discrete method      113Ч117
Collocation method, discrete collocation method      222
Collocation method, singular integral equations      328
Collocation method, superconvergence, collocation at Gauss points      59Ч63
Collocation method, superconvergence, discrete collocation method      64
Collocation method, superconvergence, for piecewise polynomials      58Ч59
Collocation method, superconvergence, for Volterra equations      117Ч120
Collocation method, superconvergence, iterated collocation method      56Ч63
Collocation method, superconvergence, versus iterated Galerkin method      63Ч64
Collocation method, zeros as collocation points      229
Compound integration rule      117
Conjugate gradient method      26
Consistency conditions      317
Convergence analysis, of projection methods      81Ч84
Convergence theorems and singular integral equations, collocation method      328 349Ч356
Convergence theorems and singular integral equations, discrete Galerkin method      356Ч359
Convergence theorems and singular integral equations, Galerkin method      323Ч328
Convergence theorems and singular integral equations, Galerkin Ч Petrov method      342Ч348
Convergence, Cauchy singular integral equations      272Ч296
Convergence, Cauchy singular integral equations, mean square convergence of Galerkin method      273Ч281
Convergence, Cauchy singular integral equations, of collocation method      284Ч287
Convergence, Cauchy singular integral equations, of discrete Galerkin method      287Ч293
Convergence, Cauchy singular integral equations, of Gaussian quadrature method      293Ч296
Convergence, Cauchy singular integral equations, Sloan iterate      283Ч284
Convergence, Cauchy singular integral equations, uniform convergence of Galerkin method      281Ч283
Convergence, Fromme Ч Goldberg rule and      224Ч225 227
Convergence, Gaussian quadrature method      235Ч236 293Ч296
Correction step      27
Data functional strategy, Abel integral equations      402Ч403
Degenerate kernel methods, Cauchy singular integral equations      207Ч209
Degenerate kernel operator      207
Dellwo Ч Friedman method, perturbed Dellwo Ч Friedman method      95
Direct boundary integral equations, Laplace equation reformulation      4Ч5 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      287Ч293
Discrete Galerkin method, superconvergence      55
Discretization error      327
Earth satellite orbits, equation for      148Ч149
Earth satellite orbits, in numerical method in astrodynamics      148Ч149
Eigenvalue problem      37
Erdoes Ч 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 Ч Goldberg quadrature rule      224Ч225
Fundamental function Z      314Ч315
Fundamental theorem of calculus      136
Galerkin method      77Ч80 95Ч106
Galerkin method, boundary integral equation reformulations      10 12 15
Galerkin method, Cauchy singular integral equations      209Ч220 262Ч263
Galerkin method, convergence, mean square convergence      273Ч281
Galerkin method, convergence, of discrete Galerkin method      287Ч293
Galerkin method, convergence, uniform convergence      281Ч283
Galerkin method, direct analysis with quadrature errors      106Ч110
Galerkin method, discrete Galerkin method      213 219 327
Galerkin method, discrete Galerkin method, convergence of      287Ч293
Galerkin method, for positive-definite dominant part equations      120Ч126
Galerkin method, in numerical method in astrodynamics      158Ч161 164Ч165
Galerkin method, iterated Galerkin method      327 348
Galerkin method, perturbed Galerkin method      141 158Ч161 164Ч165
Galerkin method, perturbed Galerkin method, in numerical method in astrodynamics      158Ч161 164Ч165
Galerkin method, singular integral equations      323Ч328
Galerkin method, superconvergence      36 38Ч40
Galerkin method, superconvergence, discrete Galerkin method      55
Galerkin method, superconvergence, iterated Galerkin method      51Ч53 55
Galerkin method, superconvergence, linear functions of Galerkin approximation      48Ч51
Galerkin method, superconvergence, versus iterated collocation method      63Ч64
Galerkin Ч Petrov method      211Ч212
Galerkin Ч Petrov method, singular integral equations      342Ч348
Gauss points, collocation at      59Ч60
Gauss points, quadrature points      79
Gauss Ч Legendre quadrature rule      133
Gaussian elimination      403Ч404
Gaussian gravitational constant      146
Gaussian quadrature formula      24Ч25 37
Gaussian quadrature method, Cauchy singular integral equations      236Ч241 264Ч266
Gaussian quadrature method, convergence      235Ч236 293Ч296
Gaussian rules      231Ч232 263
Generalized airfoil equation, analytical solution of      185Ч190
Generalized airfoil equation, mapping properties of airfoil operator      198Ч204
Generalized airfoil equation, numerical methods for      193Ч194
Generalized airfoil equation, operator formulation      204Ч207
Geometric probability, Abel integral equations      377
Gibbs-type phenomenon      214
Global methods, boundary integral equation reformulations      12Ч14
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      138Ч140
HMP method, superconvergence      53Ч55
Hodograph technique      369
Hohmann orbit      175
Indirect boundary integral equations, Laplace equation reformulation      5Ч7
Inner-product space      74
Interferometry, Abel integral equations      377
Iterated collocation method, superconvergence      56Ч58
Iterated collocation method, superconvergence, for piecewise-polynomial spaces      58Ч63
Iterated collocation method, superconvergence, versus iterated Galerkin method      63Ч64
iterated Galerkin method      327 348
Iterated Galerkin method, superconvergence      51Ч53 55
Iterated Kantorovich method, superconvergence      45Ч48
Iterated Kantorovich regularization, as variant of projection method      88Ч89
Iterated projection method, superconvergence      40Ч45
Iterative methods, boundary integral equations      25Ч29
Iterative methods, two-grid methods      26Ч29
Jacobian of the transformation      17
Kalandiya's method, Cauchy singular integral equations      247Ч249
Kantorovich method, iterated method      45Ч48
Kantorovich method, perturbed method      93Ч94
Kantorovich regularization      45
Kantorovich regularization, as variant of projection method      87Ч88
Kantorovich regularization, Cauchy singular integral equations      241Ч246
Kantorovich regularization, iterated regularization      88Ч89
Kantorovich theorem      153 157
Keplerian motion, in numerical method in astrodynamics      147 155Ч156
Keplerian motion, Lambert's problem and      147
Keplerian motion, perturbed Keplerian motion      155Ч156
Keplerian motion, two-body problem      147
Khevedelidze theorem      317
Kutta condition      191Ч193 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      4Ч5
Laplace equation reformulations, integral equation reformulations, indirect BIE methods      5Ч7
Laplace equation reformulations, integral equation reformulations, piecewise smooth boundaries      8Ч9
Laplace equation reformulations, integral equation reformulations, Poisson equation      9
Laplace equation reformulations, integral equation reformulations, smooth boundary case      7Ч8
Legendre polynomials      77
Legendre polynomials in numerical method in astrodynamics      136Ч138
Leibnitz formula      135
Lifting line theory      370
Linear functions of Galerkin approximation, superconvergence      48Ч51
Lobatto quadrature, Cauchy singular integral equations      266Ч268
Lobatto rules      117
Mean square convergence, Galerkin's method      273Ч281
Mean square convergence, Galerkin's method, $\nu=1$      278Ч281
Mean square convergence, Galerkin's method, direct method      276Ч278
Mean square convergence, Galerkin's method, indirect method      273Ч276
Motion, equations of, astronomical units in      146
Motion, equations of, earth satellite orbits      148Ч149
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 Ч Kelvin boundary value problem      363Ч364
Newton universal gravitational constant      145
Newton Ч Kantorovich method, astrodynamics numerical technique      133 141Ч144
Newton Ч Kantorovich method, iteration      157 165Ч167
Noether operators      319
Nonlinear integral equations, superconvergence      64Ч66
Numerical method in astrodynamics      see also "Motion equations
Numerical method in astrodynamics, equation of motion      144Ч149
Numerical method in astrodynamics, Green's function      132
Numerical method in astrodynamics, mathematical preliminaries      134Ч135
Numerical method in astrodynamics, mathematical preliminaries, Hilbert space      138Ч140
Numerical method in astrodynamics, mathematical preliminaries, integral equation and      135Ч136
Numerical method in astrodynamics, mathematical preliminaries, Legendre equation and      136Ч138
Numerical method in astrodynamics, mathematical preliminaries, Newton Ч Kantorovich method      141Ч144
Numerical method in astrodynamics, mathematical preliminaries, operator equations      140Ч141
Numerical method in astrodynamics, numerical examples, Earth-Mars trajectories      174Ч177
Numerical method in astrodynamics, numerical examples, trajectory optimization      177Ч178
Numerical method in astrodynamics, parallel algorithms      165Ч174
Numerical method in astrodynamics, parallel algorithms, constant vector setup in      168Ч169
Numerical method in astrodynamics, parallel algorithms, Legendre polynomial expansion      171Ч172 173
Numerical method in astrodynamics, parallel algorithms, matrix setups in      167Ч168
Numerical method in astrodynamics, parallel algorithms, solution of linear system      170Ч171
Numerical method in astrodynamics, perturbed Galerkin method      158Ч161 164Ч165
Numerical method in astrodynamics, perturbed Galerkin method, analytic principle in      163Ч164
Numerical method in astrodynamics, perturbed Galerkin method, convergence result      164Ч165
Numerical method in astrodynamics, perturbed Galerkin method, equivalence in      161Ч163
Numerical method in astrodynamics, well-posedness issue      149Ч150
Numerical method in astrodynamics, well-posedness issue, method of patched conics      151Ч152
Numerical method in astrodynamics, well-posedness issue, Newton Ч Kantorovich iteration      157 165Ч167
Numerical method in astrodynamics, well-posedness issue, perturbed Keplerian motion      155Ч156
Numerical method in astrodynamics, well-posedness issue, Picard iteration      154Ч155
Numerical method in astrodynamics, well-posedness issue, Voyager II example      152Ч153
Nystroem method      77 110 131 133 158 161 162Ч163 165
Panel method      21
Parallel processing      150 see
Parseval theorem      312Ч313 343
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