Anderssen R.S., de Hoog F.R., Lukas M.A. — The application and numerical solution of integral equations :: Электронная библиотека попечительского совета мехмата МГУ

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Anderssen R.S., de Hoog F.R., Lukas M.A. — The application and numerical solution of integral equations

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Название: The application and numerical solution of integral equations

Авторы: Anderssen R.S., de Hoog F.R., Lukas M.A.

Аннотация:

A comprehensive, up-to-date, and accessible introduction to the numerical solution of a large class of integral equations, this book builds an important foundation for the numerical analysis of these equations. It provides a general framework for the degenerate kernel, projection, and Nyström methods and includes an introduction to the numerical solution of boundary integral equations (also known as boundary element methods). It is an excellent resource for graduate students and researchers trying to solve integral equation problems and for engineers using boundary element methods.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1980

Количество страниц: 259

Добавлена в каталог: 12.01.2010

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Предметный указатель

"Flapping wing" problem      26
Abel      2
Abel integral equation - first kind      195 199 209
Abel integral equation-inversion formula      197
Acoustic and electromagnetic problems      29
Acoustic waves      86
Airfoil equation      23
Airfoil theory      22
Antenna      223
Autoregressive moving average process      238
Basis functions      62
Bateman method      67
Betti's elastic reciprocal theorem      141
Block-by-block method      187
Boundary conditions - Dirichlet      30 138
Boundary conditions - natural      159 165
Boundary conditions - Neumann      30 138
Boundary integral equation      32
Boundary integral equation discretization      34
Boundary value problem - exterior      223
Cauchy integral      5
Cauchy integral equation      21
Cauchy integral equation - first kind      38
Cauchy integral equation - numerical solution      32
Cauchy integral equation - second kind      37
Cauchy principal value      5 23 138 142 145
Characteristic value      11
Chebyshev points      41 59
Clenshaw — Curtis points      56
Collectively compact operators      12 55
Collocation method      60 112 230
Collocation-iterated method      61 99
Compact operator      53 84
Completely continuous operator      53
Conditioning      123
Consistency      165
Constant - determination of      42
Cross-validation      178
Cross-validation - weighted      178
Cumulative data      199 202
Cumulative distribution      196
Current distribution      95
Data functional      197 201 205 209 212
Deferred correction      187
Degenerate kernel method      67 70
Density data      202 212
Density distribution      197
Difference approximation      116
Differential operator      152 156 173
Direct boundary integral equation      135 138 142
Direct boundary integral equation - numerical solution      144
Dirichlet problem      121
Dirichlet problem - exterior      88-94
Dirichlet problem - interior      4 38 88—94
Discrete-time models      237
Divided difference      169 171
Double layer potential      7 38 77
Double pole equation      45
Econometrics      250
Eigenfunction      11 122 166
Eigenvalue      11 122 166 179
Elasticity      22 135 139
Elasticity - non-zero body forces in      146
electric field      86
Electric field integral equation      225
electromagnetic field      223
Euler — Lagrange equation      154 165
Extrapolation - Richardson's extrapolation      187
Filter - low pass      180
Filtering      13 242
Finite differences      32
Finite elements      32
Fluorescence decay      245
Fourier transform      2
Fredholm      10 51 75
Fredholm alternative theorem      10 53 84
Fredholm integral equation - first kind      5 30 89 119 138 151 210
Fredholm integral equation - first kind, discretization      124
Fredholm integral equation - first kind, nonlinear      223
Fredholm integral equation - second kind      7 51 75 103 138 154 158 167
Fundamental solution      136 141
Galerkin - iterated approximation      69 108
Galerkin method      68 103 106 128
Gauss points      57 111
Gradient search      228
Green's function      28 29 30 154 167 174 225
Green's theorem      79 137
Hadamard principle value      44
Hankel function      30
Harmonic function      78
Heat conduction problems      29
Helmoltz equation      30 82 224
Hermite cubic splines      113
hilbert      11
Hilbert equation of the first kind      8
Hilbert — Schmidt expansion      178
Hilbert — Schmidt theory      123
Hooke's law      140
Hydrograph      235 238 247
Identification      238
Ill-posed      121 122 151
Improperly posed      121 122 151
Improperly posed-weakly improperly posed      196
Impulse response estimation      236 245
Impulse response function      235
Inhomogeneous media      32
Input estimation      240 242
Instability      119 186 190 226 240
Instrumental variable      238 252
Integral operators - regularity of      144
Interpolating function      57
Interpolation problem      168 170 176
Interpolation-piecewise polynomial      58 62
Interpolation-polynomial      59 62
Interpolation-trigonometric      64
Interscan microwave landing system      229
Inverse scattering problem      223
iterated kernel      9
Kalman filter      242
Kernel - difference      40
Kernel - Gaussian      120

Kernel - logarithmic      39
Kernel - potential type      85
Kernel - separable      196
Kernel - singular      139 144
Kernel - symmetric      11
Kernel - weakly singular      3 53
Kutta condition      24 42 43
Landweber iteration      132
Laplace transform      2 235 236
Laplace's equation      22 76 135 136
Least squares      127 252
Limb-darkening equation      211
Line vortex distribution      26
Linear functional      195 197
Linear programming      128
Liouville      4
Magnetic field      94
Magnetic field integral equation      225
Magnetic flux density      96
Maxwell's equation      96 224
Metallurgy      198
Microwave reflector      223
Moments      195
Natural interpolation formula      54
Navier's equations of equilibrium      140 141
Nekrasov's equation      9
Neumann problem - exterior      88—94
Neumann problem - interior      88—94
Neumann's series      10
Newton's method      223 229
Noise      130 167 191 196 237
Non-homogeneous materials      146
Non-linear integral equations      14
Number density      198
Nystrom method      54 111
Pade approximant technique      71
Petrov — Galerkin - iterated approximation      70
Petrov — Galerkin method      70
Planing surfaces      31
Poisson's equation      146
Potential theory      4 76 135 136
Prandtl lifting line equation      25
Prediction error      179
Probabilistic methods      132
Product integration      57 111 125 202 212
Properly posed      121 155 201
Quadratic programming      128
Quadrature      56 124 165 184
Radiation condition      88 225
Random plane section      199
Reflector synthesis      223 227
Regularization      129 151 156 232 243 244 246
Regularization - discrete      163
Regularization - Tikhonov      153
Regularization parameter      129 152 178 243
Regularized solution      155 159
Reproducing kernel      169
Reproducing kernel Hilbert space      169
Resolvent kernel      9
Robin problem - exterior      88-94
Robin problem - interior      88-94
Shape functions      145
Single layer potential      4 77 88
Singular function      122 166
Singular value      122 166
Singular value decomposition      122 166
Singular value decomposition - truncated expansion      128
Singularity-algebraic      42
Singularity-Cauchy      30
Singularity-double pole      28
Singularity-logarithmic      38 43
Singularity-square root      41
Singularity-weak      106
Size classes      212
Size distribution      198 212
Skin effect      94
Smoothing problem      168 172 176
Sobolev Norm      152
Sobolev space      104 154
Somigliana's identity      142
Space discretization      32
Spectral filtering      243
SPLINE      104
Spline - B-spline      169 172
Spline - natural      168 177
Spline approximation      105
Stability theory      164
Stabilization of equations      128
Stabilizing functional      152
Step function discretization      35
Stereology      198
Stochastic systems      238
Stokes flow      28
Strain-displacement relations      140
Stress equilibrium equations      139
Stress-strain relations      140
Superconvergence      66 103 107
Superinterpolation      112
Surface distribution      77
Systems identification      238
Thin wing theory      25
time constant      241 245
Time series      238
Transfer function      235
Transport functionals      246
Truncation error      127
Truncation error - asymptotic expansion of      127
Variational formulation      151
Vector potential      96
Viscous fluid problems      27
Volterra      9
Volterra integral equation - Abel-type      195
Volterra integral equation - direct methods      184
Volterra integral equation - first kind      183
Volterra integral equation - first kind, convolution      235
Volterra integral equation - second kind      4 183
Volterra integral equation - stability      186 190
Water-wave problems      31
Water-wave reflection      32
Well posed      121 155 201
Z transform      237

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