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| Collatz L. — The numerical treatment of differential equations |
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| Предметный указатель |
 -extrapolation 144 154 See
Ablation 309
Abstract space 34 42
Adams extrapolation method 83 91 112 124 125
Adams extrapolation method, error estimates for 105 107
Adams interpolation method 78 85 98 126 131 137 139
Adams interpolation method, error estimates for 103 105 108 133
Adams, J.C. 78 83 536—537
Admissible function 202 213 229 425 485
Aerodynamics 286 318
Agmon, S. 329
Aitken, A.C. 162
Albrecht, J. 65 71 293 347 449 546 554
Allen, D.N. de G. 136 154 334 364
Analytic solutions 522
Antisymmetry 394
Applied mathematician 64
Approximate characteristics 324
Approximate differential equation 55 316
Approximate error limits 103 180 299 349 See
Approximation function 28
Approximation parameters 28
Arbitrary mesh 263 370
Aronszajn, N. 239
Asymptotic series 223
Averaging procedure for the heat equation 267 280 284
Averaging procedure, Liebmann's 348 356
Backward difference quotient 263 269 274 275
Backward differences 7
Baggott, E.A. 48
Banach, St. 35
Bashforth, F. 83
Bateman, H. 397 498 500
Batschelet, E. 346
Bauersfeld, K.H. 263
Beam see "Bending" "Vibrations"
Beck, E. 19 54
Bending moment 143 152
Bending of a beam 221
Bending of a plate 359 391 406 409 421 431 434 453
Bending of a strut 143 155 163 168 182 188 195 209 224
Bending of an elastically mounted rail 152 219
Berger, E. 406
Bergman, St. 286 403 419
bernoulli 403
Bernstein, Dorothy L. 262
Bertram, G. 239
Bickley, W.G. 364 380
Bieberbach, L. 71
Biezeno, C.B. 4 251 358
Biharmonic boundary-value problems 26 406 409 432 See
Biharmonic operator 26 389
Blaess, V. 70
Blasius equation 140 See
Bleich, F. 520
Block relaxation 155 158 364
Block relaxation, generalized 365
Boedewadt, V.T. 223
Bolza, O. 208
Boundary collocation 28 413
boundary conditions 2 et seq.
Boundary conditions for elliptic differential equations 24
Boundary conditions of the 1st 2nd and 3rd kinds 4
Boundary conditions, essential 4 206 216
Boundary conditions, homogeneous 4
Boundary conditions, inhomogeneous 4
Boundary conditions, linear 4
Boundary conditions, natural 432
Boundary conditions, non-linear 3
Boundary conditions, Sturm's 4
Boundary conditions, suppressible 4 206 216
Boundary expression 215 240
Boundary methods 28 413 417
Boundary pivot 344
Boundary point 345
Boundary terms 203 206
Boundary, mesh 345
Boundary-layer problem 75 130 138 333
Boundary-maximum theorem 329 396 See
Boundary-minimum theorem 398
Boundary-value problem 2 et seq. 141 342
Boundary-value problem, completely homogeneous 5
Boundary-value problem, first 25 344 355 399 427 437 441
Boundary-value problem, homogeneous 4
Boundary-value problem, linear 3 6
Boundary-value problem, mixed 346
Boundary-value problem, monotonic 41 48 200 408
Boundary-value problem, non-linear 38 47 75 145 159 179 184 198 201 212 226 252 453
Boundary-value problem, number of solutions 3
Boundary-value problem, second 25 346 355 449
Boundary-value problem, third 25 346 401 427 437 449
Bracketing 42 353 444 See "Monotonic
Bracketing of eigenvalues 228 233 248 252 502 503 527
Bracketing of solutions by relaxation 159 364
Brock, P. 83
Brouwer's fixed-point theorem 43
Brouwer, L.E.J. 43
Brueche, E. 125
Bruwier, L. 378
Bueckner, H. 238 250 479
Build-up of errors 270
Bukovics, E. 70 71
Cable, electric 324 335
Cage 367
Calculus of variations 202
Carslaw, H.S. 273
Carson, J.R. 513
Cauchy integral 505
Cauchy kernel 505
Cauchy principal value 505 530
Cauchy, A.L. 54 et seq. 324 505 530
Central difference quotient 263 269 273 274 311 315
Central differences 7 264
Central-difference method 57 78 86 94 98 105 128 132 135
Challis 83
Change, iterative 157 361
Characteristic curves 308 321
Characteristic equation 99 106 307 309
Characteristic roots of a matrix 99 121 See
Characteristic strips 307
Characteristics method of 318 323 335
Characteristics of a partial differential equation 261 295 311 320
Characteristics, magnetic 91
Charge distribution 335
Chebyshev's quadrature formula 470 475 477
Chebyshev, L. 470 475 477
Checking by differencing 72
Checking techniques 2 72 209
Checks 1
Checks, current 2 72
Checks, row-sum 269 276 280 294 326 339 341
Checks, terminal 52 72
Churchill, R.V. 273
Co-normal 23
Coil 91
Collatz, L. 25 42 45 89 90 99 101 110 111 117 135 162 177 228 229 234 236 240 246 304 329 330 365 380 385 462 468 479 492 503
Collocation 28 29 32 181 411 453 483 495 See
Collocation points, choice of 29 183 411 466
Column calculation, simplification of 55
Combined methods 31
Combined methods, Collocation and iteration 34 195 481
Combined methods, iteration and error distribution 33
Combined methods, least-squares 31
Combined methods, Ritz 208
comparison function 229
Comparison of solutions with different steps 51 52 71 75 144 154 169
Comparison theorem 236
Complete abstract space 35 37
Complete system of functions 30 222 422
Completely homogeneous boundary-value problem 5
| Complex integration, formulae for 96
Complex solutions 252
Conformal transformation 507
Conjugate potential function 355
Connectivity of a mesh 345
Consistency conditions 322
control systems 521
Convergence of iterative processes 38 97 190 250 478 516
Convergence of main iteration 89 97 104 131
Convergence of power series 225
Convergence of single-step iteration 46 173 174
Convergence of starting iteration 99 120
Convergence of step-by-step methods 59 60 61
Convergence of total-step iteration 46 173
Convolution-type kernel 492 513
Cooperman, Ph. 406
Courant, R. 25 60 228 262 295 296 301 306 318 319 343 396—398 453 468
Craggs, J.W. 112
Current checks 2 72
Curved boundaries 345—347
Darby, P. 360
Decomposition of a matrix 44 173 372
Decomposition of finite-difference equations 372
Defect 42 115
Definiteness of a quadratic form 174
Definiteness of distance 34
Deflection see "Bending"
Degenerate kernel 498 511
Dependence, domain of 295
Determinate region 295 311
Determinate region, finite-difference 295 311
Diagonal mesh 374
Diaz, J.B. 348 406 407 434 444
Difference equations, linear 105
Difference method see "Finite-difference"
Difference operators 7 264
Difference quotients 141 263 343
Difference quotients, backward 263 269 274 275
Difference quotients, central 263 269 273 311 315
Difference quotients, forward 263 265 273 311
Difference table 7
Difference table, horizontal 8 84
Difference table, sloping 7
Differences 7 72
Differences, backward 7
Differences, central 7 264
Differences, forward 7
Differences, higher 7 72
Differential equation in the complex plane 95
Differential equation, disturbed 187
Differential equation, elliptic 24 43 329 344 396
Differential equation, homogeneous 4 6
Differential equation, hyperbolic 277 295 321 324 329 335
Differential equation, implicit 96
Differential equation, inhomogeneous 4 6
Differential equation, linear 3 6 306 344
Differential equation, mixed-type 286 329
Differential equation, non-linear see "Non-linear"
Differential equation, parabolic 265 280 284 295 329
Differential equation, partial 5
Differential equation, quasi-linear 6 306 308 319
Differential equation, self-adjoint 208 216 435 446
Differential equation, stability of 112
Differential equation, systems of 110 116 153 265 305
Differential equation, transformation of 96 117 137 208
Differential operators 18
Dirichlet boundary expression 240
Dirichlet integral 437 440
Dirichlet, P.G.L. 240 348 437 440
Discontinuous solutions 522
Distance in function space 34 38 198
Disturbed differential equation 187
Doetsch, G. 273
Domain of admissible functions 202 213 425 485
Domain of dependence 295
Double series 419 421 423
Duff, G. 306
Duffing's method 54 137 318
Duffing, G. 54 137 318 536
Duncan, W.J. 32
Dusinberre, G.M. 364
Eddy current density 272
Eddy, R.P. 302
Eigenfunction 5 41 150 212 231 423 467
Eigenfunction expansion 190 246 250 422
Eigenvalue problems for functional-differential equations 528
Eigenvalue problems for integral equations 467 472 474 479 495 502
Eigenvalue problems for ordinary differential equations 5 147 163 170 210 227
Eigenvalue problems for partial differential equations 373 392 395 422 452
Eigenvalues 5 467
Eigenvalues of a matrix see "Characteristic roots" "Latent
Eigenvalues, bracketing of 228 233 248 252 502 503
Elastic mounting 152 219
Elastic thread 453
Electric cable problem 324 335
Element of an abstract space 34 42
Elliptic differential equation 24 43 329 344 396
Elliptic function 145
Elser, K. 284 285
Eltermann, H. 113
Enclosure theorem 236 252 503 527
Energy distribution 520
Engel, F.V.A. 522
Enskog, D. 493
Error distribution methods 28 See
Error distribution principles 29 410 442 482
Error distribution principles, combination of 31
Error estimates See also "Bracketing" "Error
Error estimates for boundary-value problems 176—177 196 348 364 399 401 407 416 446 449
Error estimates for eigenvalue problems 479 See
Error estimates for initial-value problems 51 57—61 71 97 111 113—114 133 296 299 329 331
Error estimates for iterative processes 38 97 115 196 199 353 479
Error estimates for starting values 103 109 122
Error estimates, independent 59—61 105 134
Error estimates, recursive 59—61 101 133
Error estimation by the boundary-maximum theorem 399 et seq. 418 446 449
Error estimation by the general iteration theorem 38 114 191 481
Error estimation with monotonic problems 202 331—333 416
Error estimation with power series solution 226
Error estimation with relaxation 42 364
Error function 29
Error in approximate values 57—58
Error propagation 264 268—276 301—305
Essential boundary conditions 4 206 216
Estimation of high order derivatives 103 177 179 349
Euler — Cauchy method 54 60 324
Euler — Maclaurin quadrature formula 54
Euler's conditions 203
Euler's differential equation 203 215 426 436 440 484
Euler's equations for the motion of a top 75
Euler, L. 53 et seq. 75 203 252 324 426 485 540 541
Existence of solutions 37 43 307 348 512
Explicit methods see "Extrapolation methods"
Extrapolation formulae in the complex plane 95
Extrapolation methods 78 83 123 See "Falkner" "Nystroem" "Stormer"
Extrapolation to infinite interval 150
Extrapolation with Liebmann's iteration 357
Falkner's extrapolation method 124
Falkner, V.M. 124
Federhofer, K. 406
Fejer, L. 398
Feshbach, H. 504
Fichera, G. 397 449
Finite boundary conditions 274
Finite differences 6
Finite equation 141 287
Finite expression 160 378
Finite-difference determinate region 295 311
Finite-difference method, ordinary 141 262 342
Finite-difference method, ordinary, graphical procedure for 280 284
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