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| Collatz L. — The numerical treatment of differential equations |
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| Предметный указатель |
Mesh, arbitrary 263 370
Mettler, E. 438
Meyer zur Capellen, W. 186
Meyer-Eppler, W. 520
Mikeladze, Sh. 167 386
Milne, W.E. 49 78 80 88 111 341 342 346 357 373 520 536 537
Milne-Thomson, L.M. 520
Mineur, H. 49
Minimum principles 239 433
Miranda, C. 407
Mises, R.V. 101 102 154 174 262 348 370 397 419 441 467 468 508 527
Mitchell, A.R. 112
mixed boundary-value problem 346
Mixed extrapolation-interpolation methods 88
Mixed methods 28 See
Mixed Ritz method 273 438
Mixed-type differential equation 286 329
Mlak, W. 302
Mohr, E. 77
Monotonic boundary-value problems 41 48 200 408
Monotonic matrix 43 110 123 133 352—353
Monotonic matrix, conditions for 43—45
Monotonic operators 42
Monotonic problems 42
Monotonic problems in parabolic equations 329
Monotonic systems of linear equations 43—47 110 173 178 348
Morse, P. 504
Motzkin, T.S. 398
Multhopp, H. 511 512
Multiple eigenvalues 230
Multiple integrals see "Repeated integration"
Murray, F.J. 83
Muskhelishvili, N.J. 505
Nagy, B.v.Sz. 186
Natural boundary condition 432
Natural frequencies 147
Natural step length 89
Neighbouring boundary-value problem 186 198
Neighbouring points 344
Neumann, J.V. 302 419 478
Newton's interpolation formula 8—11 14
Newton's iteration (Newton — Raphson) 521
Newton, I. 8 et seq. 521
Nicolovius, R. 406
Nirenberg, L. 329 330
Nodal lines 394
Noerlund, N.E. 520
Non-decomposable matrix 44 173 178 348
Non-equidistant pivotal points 162 See
Non-linear boundary-value problems 38 47 75 145 159 179 184 198 201 212 226 252 453
Non-linear integral equations 43 477 480 481 483 488 497 527
Non-linear oscillations 198
Non-linear parabolic differential equations 329—333
Non-linear systems of equations 146 159 180 212 462—464 477 484 489 523 530
Non-linear systems of equations, solution by iteration 463 478 530
Non-linear systems of equations, solution by recursion and interpolation 146
Non-linear systems of equations, solution by relaxation 159 464
Non-trivial solution 5 484
Norm 35 40 114 192 196 482
normal 21
Normal derivative 24
Normal modes 452 See
Normalization, generalized 246
Novozilov, V.V. 33
Numerov 167
Nystroem's extrapolation method 84 108
Nystroem, E.J. 65 84 108 166 470 537
O'Brien, G. 301
Oberkettinger, F. 510
Obreschkoff, N. 19
Oldenbourg, R.C. 522
Operational methods 273
Operator for boundary-value problems 39 47 192
Operator for initial-value problems 114
Operator for integral equation 481
Operator for parabolic equations 330
Operator method 378
Operator, abstract 35
Operator, biharmonic 26 389
Operator, difference 7 264
Operator, differential 18 378
Operator, displacement (shift) 378
Operator, Laplace's 22 346 374 386 389
Operator, Lipschitz-bounded 36
Operator, monotonic 42
Oppolzer, T.R.v. 131
Optical image 527
Order of an approximate method 51
Order of Duffing's method 137
Order of the Runge — Kutta method 68
Orthogonal functions 223 493
Orthogonality method 30—32
Orthogonality, generalized 230
Oscillating temperature distribution 268 334
Oscillation, forced 198
oscillations see also "Vibrations"
Oscillations of a suspension bridge 492
Oscillations, non-linear 137 198
Oscillations, small 137 525
Ostrowski, A.M. 43 130
Oswatitsch, Kl. 319
Over-relaxation 363
Parabolic differential equation 265 272 280 288 291 329
Parabolic differential equation with three independent variables 284
Particular solutions 403
Partition method 30 33
Periodic solutions 198 334 525
Perron, O. 162
Perturbations 111 135
Perturbations method 186
Pflanz, E. 19 54 162 318
Picone, M. 30 329 449
Pincherle, S. 519
Pivot 344
Pivot, boundary 344
Pivot, interior 344
Pivotal interval 141
Pivotal points 141
Pivotal values 142 263
Pivotal values, exterior 142 359 380
Plate problems see under "Bending" "Boundary "Temperature
Poeschl, Th. 209
Point relaxation 158
Poisson's equation 369 371 381 386 405 410 414 417 419 422 439 445 447 451
Poisson, S.D. 386 397
Pollaczek-Geiringer, Hilda 102 154 174
Polygon method 53 58
Polygon, funicular 167 189
Poritzky, H. 438
Positive definiteness of a kernel 502
Positive definiteness of a matrix 24
Positive definiteness of a quadratic form 174
Positive definiteness of distance 34
Potential equation 445 470 See "Poisson's
potential flow 355 380 387
Potential function 355
Power series 91 137 223 261 310 419 518 523 528 See
Prandtl's circulation equation 511
Prandtl's stress function 451
Prandtl, L. 64 441 451 511
Predictor-corrector methods see "Mixed extrapolation-interpolation methods"
Propagation of errors 49 270—276 301—305
Propagation table 270
Protter, M.H. 286 329
Pseudo-metric space 38
Pucci, C. 401
Quade, W. 79 83 536
Quadratic form 174
Quadratic function 174 215
Quadrature error 60 61
| Quadrature formulae 72 81 118 316 469 See "Euler "Gauss" "Integration" "Simpson" "Three-eighths "Trapezium
Quasi-linear differential equation 6 306 308 319
Radial stress 251
Rail, elastically mounted 152 219
Railway track mountings 493
Rayleigh — Ritz method 248 See
Rayleigh's minimum principle 239
Rayleigh's quotient 230
Rayleigh, J.W. 230 et seq. 239
Rectangular mesh 263 343
Rectangular plate 434
Recursion formula 225 261
Recursive error estimates 59—61 101 133
Recursive solution of systems of linear equations 144 150 153
Recursive solution of systems of non-linear equations 146
Reduced system of finite-difference equations 372
Reduction to boundary-value problem 136 333
Reduction to coarser mesh 374
Reduction to explicit differential equation 96—97
Reduction to initial-value problem 77 184
Reduction to ordinary differential equations 265 305 439 440
Reduction to plane problem 369 452
Rees, Mina 296
Regular integral equation 467
Reissner, M.E. 493
Relaxation 30 42 154 360
Relaxation and monotonic problems 42
Relaxation with error estimation 42 364
Rellich, F. 186
Repeated integration 11—17 52
Residuals 30 42 154 361
Response of a linear system 514
Richardson, L.F. 343 364
Richter, W. 61 110
Richtmyer, R.D. 302
Rigorous error limits 51 102 See
Ritz approximation 207
Ritz approximation, mixed 438
Ritz method 202 241 245 252—253 400 425 441 444 453 484—489 527—528
Ritz method, mixed 273 438
Ritz, W. 1 4 202 239 425 527
Roberts, R.C. 348
Rod, steady temperature distribution in 150 159 182
Rod, unsteady heat flow in 267 281 293 333—335
Rosenbloom, P.C. 38
Rotating disc 251
Rothe, E. 43
Rounding error 50 57 102 112 267
Rounding off 267
Row-sum checks 269 276 280 294 326 339 341
Row-sum criterion, ordinary 45 46
Row-sum criterion, weak 45 46 173—175 348
Runge — Kutta method 50 57 61—78 80 94 118 137 138
Runge — Kutta method, stability of 112
Runge, C. 48 et seq. 61 137 343 371 441 537
Runge, Iris 64
Rutishauser, H. 111 112 135
Salzer, H.E. 95 96
Sanden, H.v. 49 50 72
Sartorius, H. 522
Sassenfeld, H. 171
Sauer, R. 262 306 318 319
Scarborough, J. 48
Schaefke, Fr.W. 186
Schauder, J. 43
Schiffer, M. 419
Schlichting, H. 77
Schmeidler, W. 468
Schmidt, Erhard 521
Schmidt, Ernst 281
Schroeder, J. 38 186 198 372 373
Schroeder, K. 511
Schultz-Grunow, F. 319
Schulz, G. 8 44 49 81 101 102
Schwabe, M. 511
Schwarz constants 231 479
Schwarz quotients 231 479
Schwarz's inequality 27 114
Schwarz, H.A. 27 114 231 479
Schwarzschild 64
Seidel, Ph.L. 154
Self-adjoint differential equations 208 216 228 435 446
Self-adjoint eigenvalue problems 229
Semenov, N.S. 438
Semi-ordered space 38 42
Separable differential equation 403
Series expansion 222 418 451 492 See "Power
Severn, R.T. 136 334
Shaw, F.S. 346 361
Shear stress 358 453
Shortley, G.H. 357 360
Simpson's rule 11 87 316 470 474 477 516 528 529 530
Simpson, Th. 11 87 470 474 477 515
Single-step iteration 46 173 348 367 373
Single-term class of eigenvalue problems 236 246
Singular integral equation 468 504—512
Singular kernel 504
Singular point 208 439
Singularities, treatment of 253 275 279 286 357 380 508
Skan, Sylvia W. 411
Smoothing of irregularities 90 94
Smoothing of kernels 504
Smoothing procedure 91 94 424
Soehngen, H. 511
Solving kernel 500
Sommerfeld, A. 262 419
Sound waves 452
Southwell, R.V. 154 361 364
Spatial problems 368
Special eigenvalue problems 228 232 234 237 240 243
Spectrometer 520
Spectroscopy 520
Square cross-section 403 410 423 447
Square mesh 263
Square plate 359 361 421 431
Square wire 410
square-integrable 502
Stability condition 302 305
Stability in control systems 521
Stability of difference equations 268—276 287—288 301—305 335
Starting iteration 81 99 103 109 118—123
Starting values 79—82 117—123
Steam turbine rotor 251
Steffensen, J.F. 9 378
Stencils for finite-difference formulae 373 390
STEP 7 53
Step function, unit 514
Step index 71 89
Step length 53 79
Step length, change of 78 89
Step length, choice of 71 78 82 89 118—119 129
Step length, natural 89
Step-by-step integration 50
Step-by-step methods for integral equations 513
Stiefel, E. 231 365 367
Stirling's interpolation formula 8 et seq. 86
Stirling, J. 8 et seq. 16 86
Stoermer's extrapolation method 125 129
Stoermer, C. 101 125 129 537
Stohler, K. 90
Stracke, G. 167 168
Stream function 355
Streamlines 355
Stress distribution 251 435
Stress function 357 451
String, vibrations of 252 261 525
Strip conditions 307
Strip manifold 307
Structures, theory of 520
Strut see under "Bending"
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