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Hinton D., Schaefer P.W. — Spectral Theory and Computational Methods of Sturm-Liouville Problems
Hinton D., Schaefer P.W. — Spectral Theory and Computational Methods of Sturm-Liouville Problems

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Название: Spectral Theory and Computational Methods of Sturm-Liouville Problems

Авторы: Hinton D., Schaefer P.W.

Аннотация:

Presenting the proceedings of a recent conference on Sturm-Liouville problems held in conjunction with the 26th Barrett Memorial Lecture Series at the University of Tennessee, Knoxville, this timely volume covers both qualitative and computational theory of Sturm-Liouville problems - surveying current questions in the field as well as describing novel applications and concepts. Spectral Theory and Computational Methods of Sturm-Liouville Problems reviews boundary value problems for ordinary differential equations...details the dependence of eigenvalues on parameters of the problem, such as interval endpoints, boundary conditions, and coefficients of the equation...addresses the question of approximating singular problems by regular ones...proposes accurate approaches to software computation of eigenfunctions from a small set of values...discusses methods for eigenvalue computation of bounds and enclosures...reconstructs wavespeed in a nonhomogeneous medium from scattering data...furnishes important applications in optical fiber design, chemical photodissociation, and interface conditions...and more. Containing references, drawings, tables, and 1400 display equations, this excellent self-contained resource of active research is indispensable for theoretical and applied mathematicians; computational physicists, numerical analysts, and computer scientists specializing in scientific computing; mechanical engineers; and graduate students in these disciplines.


Язык: en

Рубрика: Математика/Анализ/Дифференциальные уравнения/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 400

Добавлена в каталог: 09.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Absolutely continuous spectrum      100 308
Adjoint systems      23
Airy function approximation      393
Asymptotic averaging      304
Band continuous spectrum      366
Behnke — Goerisch equation      98
Bessel equation      87 172 178 368
BEZ equation      89
Bound state      106 110 114
Boundary conditions, complex coupled      62
Boundary conditions, containing eigenparameter      183 371
Boundary conditions, coupled      48 51 219
Boundary conditions, Friedrichs      355
Boundary conditions, inherited      83
Boundary conditions, interface      212 224
Boundary conditions, interval      100 240
Boundary conditions, periodic      287
Boundary conditions, real coupled      61
Boundary conditions, regular      45
Boundary conditions, semi-periodic      287
Boundary conditions, separated      47 53 61 214
Boundary conditions, singular      73
Boyd equation      88
Characteristic numbers      380
Circle method      199
Coffey — Evans equation      364
Collocation      340
Comparison problem      314 321
Complete orthogonal set      254 256
Continuous dependence, eigenfunctions      57
Continuous dependence, eigenvalues      57
Continuous dependence, solutions      14 30
Continuous extension      28
Contraction mapping      5
Coupling constant      380
Deficiency indices      235
Delta interactions      245
Diagonalization approximate      204
Diagonalization exact      202
Differentiable dependence, eigenvalues      66
Differentiable dependence, solutions      16 32
Dirichlet condition      259
Dirichlet's formula      258
Discontinuous coefficients      107
Discrete spectrum      255
Dunford — Schwartz equation      94
Eigenvalue approximation      85
Eigenvalue bounds      314
Elliptic problems      325
Elliptical coordinates      379
Elliptical core fibers      378
Embedded eigenvalue      290
Enclosure intervals      313
Endpoint classification, limit circle      37 151 121 215 217 231
Endpoint classification, limit circle nonoscillatory      37 28 151 351 354
Endpoint classification, limit circle oscillatory      37 354
Endpoint classification, limit point      37 151 198 215 231 301 354
Endpoint classification, nonoscillatory      37
Endpoint classification, oscillatory      32
Endpoint classification, regular      36 78 215 351 353
Endpoint classification, weakly regular      86 353
Essential spectrum      76 83 150 288
Even and odd modes      378
Existence      3
Exponential map      21
Exponential polynomials      126
Factorization      41
Fourier equation      49
Friedrichs extension      26
Frobenius solution      267 390
Fundamental matrix      8
Generalized eigenvalue problem      136
Generalized solution      188 230
Green's formula      215 228 258
Greens function      338
Gronwall inequality      9
Halvorsen equation      88
Hardy inequality      160
Hardy spaces      116
harmonic oscillator equation      93
HELP inequality      199 207
Herglotz representation      302
Homotopy method      314 321
Hydrogen atom equation      91 364
Indefinite real matrix      136
Indefinite weight function      351 371
Interior singularities      212
Interpolant      336
Inverse eigenvalue problem      135
Inverse scattering problem      105
Jacobi equation      93
Jorgens equation      97
Jost solutions      108
Kato — Rellich theorem      150
Kato's bounds      316
Krall equation      95
L-spline approximates      341
Laguerre, differential expression      252
Laguerre, equation      96
Laguerre, polynomials      253
Laplace tidal wave equation      89
Latzko equation      89 328
Left definite theory      272
Left-definite problem      100
Legendre equation      86 363
Lehmann's method      319
Linear functional      189
Liouville transformation      111
Lohner equation      97
Marchenko integral equation      119
Marietta equation      93
Mathieu equation      90 357 380 381
Matrix of moments      137
Maximal domain      38 229 258 353
Maximal operator      74 150 229
Meissner equation      96
Minimal operator      74 150
Morse oscillator equation      94
NAG code SL02F      285 333 349
Nevanlinna function      198
Nonhomogeneous medium      106 108
normalization constant      137
Operator pencils      181
Operator, compact      189
Operator, left-definite      255
Operator, right-definite      255
Perturbation      149 288
Photodissociation      388 390
Plum equation      90
Positive definite, inner product      255
Positive definite, matrix      136
Positive definite, operator      191
Positive definite, sequence      140
Potential, long range      308
Potential, Morse      344
Potential, periodic      287 310
Potential, repulsive      390
Potential, short range      308
Potential, sparse      310
Principal solution      72
Principal submatrices      143
probability density      308
Propagation constant      378 388
Rayleigh — Ritz method      194 314 317
Reduced scattering coefficients      109
Reduced scattering matrix      110
Reflection coefficient      106 108 125
Refractive index      379
Regularizing functions      39 181
Relatively bounded      149
Relatively compact      150
Residual correction      339
Resolvent set      288
Richardson extrapolation      335
Riemann — Hilbert problem      107 114 116
Riesz basis      186
Riesz representation theorem      189
Right-definite theory      258
Scattering coefficients      107 108
Scattering data      124
Schrodinger equation      301 388
Sears — Titchmarsh equation      88
Singular spectrum      308
SLDRIVER      349 374
SLEDGE      175 285 333 349
SLEIGN      175 285 333 349
SLEIGN2      76 86 175 182 285 330 349
SLTSTPAK      350
Sobolev space      256
Spectral density function      302 305
Spectral function      136 137 198 208 286
Spectral measure      302
STANDARD problem set      352
Stieltjes inversion formula      198
Strong limit point      259
Successive approximations      5
Three term recurrence      135
Titchmarsh — Weyl function      198 232 302 377
Titchmarsh — Weyl matrix      204
Transmission coefficient      107 108
Tridiagonal matrix      136
Uniform convergence      292
Uniqueness      3 27
Unitary transformation      151 278
Variation of parameters      9
Walker method      378 386
Wave equation      106
Weakly guidring modes      385
Weinstein's bounds      315
Weyl circle      199
Weyl dichotomy      231
Whittaker equation      98
WKB solution      392
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