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| Collatz L. — The numerical treatment of differential equations |
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| Предметный указатель |
Finite-difference methods 50 78—79 202 311 451 469 526
Finite-difference methods of a higher approximation 163 375
Finite-difference methods, improved 160 et seq. 286 375
Finite-difference step-by-step methods 78 116 See "Extrapolation
Finite-sum method for integral equations 469 513 527
Finite-sum solutions of difference boundary-value problem 371
Finsterwalder, S. 308
First variation 204
Fischer, H.J. 520
Fixed point (element) 36 43
Fixed point theorem 43
Flexural vibrations 253 303 395 472
Flow problem 355 380 387 See
Fluid dynamics 333
Foeppl, A. 75
Forced oscillations 198
Forsyth, A.R. 431
Forward difference quotient 263 265 273 311
Forward differences 7
Fourier analysis 371 423 492 506
Fourier transforms 369
Fourier's integral theorem 493
Fourier, J.B.J. 493 506
Fox, L. 361
Fraenkle, A. 250
Frank, Ph. 262 397 419 467 468 508 527
Frazer, R.A. 411
Fredholm, J. 250 505
Free boundary values 215
Fried, B. 357
Friedrichs, K. 238 262 295 296 301 319 343
Frobenius, G. 121
Full symmetry 394
Full-definite 329
Function space 35
Function theory 521
Functional 203 438 440
Functional analysis 34 43
Functional equation 467 519 528
Functional-differential equation 519 521 525
Fundamental solution 27 406
Fundamental system of solutions 186
Funicular polygon 167 189
Funk, P. 406 520
Galerkin's equations 31—32 208 223 243 249
Galerkin's method 31 413
Galerkin, B.G. 31 32 208 243 249 413 449
Gamble, H. 360
Garrick, J.E. 508
Gauss's integral theorem in space 22—23
Gauss's integral theorem in two dimensions 21
Gauss's quadrature formula 470
Gauss, K.F. 21—23 154 470
Geiringer, Hilda see "Pollaczek"
General eigenvalue problem 228 244
General iteration theorem 36
Gerschgorin, S. 348 349 357
Gilles, D.C. 364
Glacier motion 308—317
Goertler, H. 286 333
Goldstein, S. 77
Grammel's equations 244
Grammel, R. 4 244 251 358 441
graphical methods 48 50 189 234 280—285 318 522
Green's formula 22 24
Green's functions 25—26
Green's functions in determining Lipschitz constants 40 191 197—199
Green, G. 21 et seq. 39 40 166 191 419 470 472
Greenberg, H.J. 406 407 434
Group relaxation 155 367
Growth of error limits 108 134—135
Growth of errors 49 50 270
Gruensch, H.J. 401
Gruesz, G. 202
Guarding figures 50 270
Guide curves 520
Gunnery problem 3
Hahn, W. 522
Hamel, G. 101 468 502
Hartree, D.R. 49 264 537
Heat equation 265 281 284 288 291 336
Heat flow problems, one-dimensional, steady 150 159 182
Heat flow problems, one-dimensional, unsteady 267 281 293 333—335
Heat flow problems, three-dimensional, steady 368 437
Heat flow problems, two-dimensional, steady 361 381 405 410 419 429 452—453
Heat flow problems, two-dimensional, unsteady 335
Heat generation, internal 159 293 410 453
Heat loss 150 334 410 452
Heinhold, J. 508
Helical spring 357 453
Hellwig, G. 286
Hencky, H. 32 343
Hermite's formula 19 20 165 318
Hermite's interpolation formula 164
Hermite, Ch. 19 79 164 318
Hermitian formulae 164 et seq. 172 291—293 384—388
Hermitian methods 164—173 175 293 384 451
Herrick, S. 131
Heun, K. 64 536
Hexagonal membrane 392
Hexagonal mesh 389
Hexagonal plate 395
Higher approximation with the finite-difference methods 160 et seq. 286 336 375
Higher derivatives 17
Higher derivatives, estimation of 103 177 179 349
Higher differences 7 72
Higher eigenvalues 230 238 245
Hilb, E. 521
Hilbert, D. 25 228 262 295 306 318 396—398 468
Hildebrand, F.B. 301 346
Homogeneous 4 et seq. 467
Honeycomb pattern 390
Hopf, E. 397
Horn, J. 262
Horvay, G. 238
Householder, A.S. 164
Huber, A. 513
Hydrodynamics 318 355
Hyman, M. 301 371
Hyperbolic differential equation 277 295 321 324 329 335
Iglisch, R. 479 503
Ill-conditioning 364
Illumination, intensity of 527
Implicit differential equations 96
Implicit methods see "Interpolation methods"
Improved Euler — Cauchy method 54 56 60 324
Improved finite-difference methods 160 et seq. 286 375
Improved polygon method 53 55 59
Incompressible flow 355 380 387
Independent error estimates 59—61 105 134
Index J 287 et seq. 300 302
Index, step 71 89
Indications of error magnitude 51—52 71 349 See
Infinite fundamental region 440
Infinite interval 150 182
Infinite systems of equations 223—224 494 523 534
Infinity, boundary conditions at 150 182 440
Inherent error 50 57 270
Inhomogeneous 4 467
Initial segment 295
Initial values 49 79 185
Initial-/boundary-value problems 260 et seq. 439
Initial-value problems 2 5 49 184 277 305
Instability of partial difference equations 264 271 301 304 335
Instability with step-by-step methods 111 135 See
Integral equations 467 See "Non-linear"
Integration formulae 9 et seq. 316 See
Integration, repeated 11 et seq. 52
Integro-differential equation 467—468 489 492 496
Intensity distribution 487
| Intensity of illumination 527
Interior collocation 28 182 411 483
Interior mesh points 343
Interior methods 28 410
Interior pivot 344
Interpolation formulae 8 et seq. 89 See "Lagrange" "Newton" "Stirling"
Interpolation methods 78 85 126 See "Central-difference" "Lindeloef"
Interpolation polynomials 8 et seq. 83
Interpolation polynomials, trigonometric 83
Interpolation with relaxation 159
Interpolation, determination of eigenvalues by 150
Interpolation, solution of non-linear boundary-value problems by 186
interval 7 141 See "Step"
Inverse element 34
Inverse matrix 43 110
Inversion formulae 510
Inward normal 21
Irregularities 90 94
Isaacson, E. 296
Iterated functions 520
Iterated kernels 503 505
Iteration See also "Convergence" "Error
Iteration in single steps 46 173 348 367 373
Iteration in total steps 46 173 348 373
Iteration theorem, general 34 36 43
Iteration with implicit step-by-step procedures 54—55 86—90 92 94 129
Iteration, Liebmann's 347 356
Iteration, starting 81 103 109 118
Iterative methods for boundary-value problems 33 39 189 195
Iterative methods for eigenvalue problems 230 249 502
Iterative methods for implicit differential equations 97
Iterative methods for initial-value problems 73 97 315
Iterative methods for integral equations 478 516
Iterative processes, general 36
Iterative solution of systems of linear equations 46 157 347 359 386
Iterative solution of systems of non-linear equations 463 477
Jaeckel, K. 512
Jaeger, J.C. 273
Jones, W.P. 411
K-definite 240
Kamke's minimum principle 239
Kamke, E. 4 48 50 96 189 215 239 262 306 519
Kantorovich, L. 36 239 438 470 508
Kaplan, S. 301
Kernel 467
Kernel function, Bergman's 419
Kieszling, F. 237
Kinetics 520
Kloeppel, K. 492
Klotter, K. 55 137
Kneser, H. 523
Knopp, K. 21
Koch, J.J. 250
Koenig, H. 48
Kopal, Zdenek 49
Kowalewski, G. 19
Kronecker, L. 499
Kryloff, N. 207
Krylov, V.I. 239 470 508 513
Kuepfmueller, K. 91
Kurepa, L. 38
Kutta, M.W. 50 57 64 536 537
Laasonen, P. 269
Lagrange 164
Lagrange's interpolation formula 164
Lagrangian form of finite-difference expressions 83
Lagrangian methods 164
Lanczos, C. 250
Laplace transform 273 369
Laplace's differential operator 22 346 374 386 389
Laplace's equation 347 349 355 361 368 371 380 387 403 437 440 451—452
Laplace, P.S. 22 273 348 513
Laplacians 457
Latent roots 373
Latent vectors 373
Lax, P.D. 286 296 302
Least-squares method 29 et seq. 138 184 220 414 442 483
Least-squares method with weighting functions 30
Lehmann, N.J. 246
Leibniz 19
Leray, J. 43
Lettenmeyer, F. 194
Leutert, W. 301
Levy, H. 48
Lewy, H. 296 301 343
Lie, H. 492
Liebmann's iteration method 347 356
Liebmann, H. 343 348 356 363
Limit element 35 37
Lindeloef's method 87 128
Lindeloef, E. 72 87 128
Lindow, M. 48
Linear boundary-value problem 3
linear combination 144 185 202 207
Linear differential equation 4 6 306 344
Linear integral equations of the 1st and 2nd kinds 467
Linear integro-differential equations 468
Linear systems of equations, monotonic 43—47 110 178 348
Linear systems of equations, solution by recursion 144 150 153
Linear transformation 514
Liniger, W. 111
Liouville 478
Lipschitz condition 40 53 110 117
Lipschitz condition, weak 113
Lipschitz constant 36 191
Lipschitz constant, determination of 36 39—42 97 114—117 191—194 197—200 482
Lipschitz function 114
Lipschitz, R. 36 et seq. 53 57 97 191
Lipschitz-bounded 36
Ljusternik, L.A. 341
Loesch, F. 494 508
Loewdin, P.O. 88
Logarithmic singularity 357 511
Longitudinal vibrations of a cantilever 147 163 170 210 235 237 248
Lorentz, H.A. 202
Lotkin, M. 54
Mach, E. 102
Maclaurin, C. 54
Magnetic characteristics 91
Magnetic field strength 272
Magnus, W. 510
Maier, E. 244
Main calculation 79 82 117 123
Mangoldt, H.V. 21
Manifold 34 307
Maple, C.G. 406
Marasimhan 330
Marcus, H. 343
Massau, J. 318
Matrix 43 99 See
Matrix, decomposition of 44 372
Maximum property 443
Mean continuity 502
Measure 442 447
Measurement problem 487
Measuring instrument, sluggish 514 516
Meissner, C. 522
Melan, E. 520
Membrane problems 278 392 417 453
mesh 263
Mesh boundary 345
Mesh co-ordinate 263
Mesh lines 263
Mesh parameter 304 335 See
Mesh points 263 343
Mesh refinement 374
Mesh relation 265 271 277 281 284 295 304
Mesh width 263
Mesh width in the complex plane 95
Mesh width, choice of 295 311
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