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



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Íàçâàíèå: Numerical Solution of Integral Equations

Àâòîð: Golberg M.A.

ßçûê: en

Ðóáðèêà: Ìàòåìàòèêà/

Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö

ed2k: ed2k stats

Ãîä èçäàíèÿ: 1990

Êîëè÷åñòâî ñòðàíèö: 430

Äîáàâëåíà â êàòàëîã: 30.11.2013

Îïåðàöèè: Ïîëîæèòü íà ïîëêó | Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
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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, $\nu=1$      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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