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| Авторизация |
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| Поиск по указателям |
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| Samarskii A.A. — The Theory of Difference Schemes |
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| Предметный указатель |
"Through execution" algorithm 691
A priori estimate 97 203 420 448
Approximation, difference 56
Approximation, difference of order m 56 69 73
Approximation, exact 74
Approximation, summarized (summed) 691
Cauchy — Bunyakovskii inequality 101
Condition,  -stability 411
Condition, Courant 376
Condition, first boundary 8
Condition, norm concordance 56
Condition, periodicity 179
Condition, second boundary 8
Condition, third boundary 8
Difference analog of the second Green formula 101
Difference derivative, central 57
Difference derivative, left 57
Difference derivative, right 57
Difference problem, Dirichlet 252
Difference problem, ill-posed 127
Difference problem, well-posed 96
Difference scheme 74 78 126
Difference scheme with increased accuracy 347
Difference scheme with increased accuracy, symmetric 303
Difference scheme with variable operators 347
Difference scheme with variable operators, well-posed 388
Difference scheme, "rhombus" 324
Difference scheme, additive 598 618
Difference scheme, alternating direction 547
Difference scheme, best 168 169
Difference scheme, co-equivalent 231
Difference scheme, co-stable 230
Difference scheme, conservative 150
Difference scheme, Crank — Nicolson 303
Difference scheme, disbalanced 150
Difference scheme, Du-Fort — Frankel 324
Difference scheme, Duglas — Rachford 629
Difference scheme, economical 349 619
Difference scheme, explicit 76 302 345 358 386 388
Difference scheme, explicit iteration 657
Difference scheme, factorized 565
Difference scheme, forward 302
Difference scheme, fully conservative 532
Difference scheme, higher-accuracy 207 290
Difference scheme, homogeneous 146 147
Difference scheme, implicit 76 386 388
Difference scheme, implicit iteration 657
Difference scheme, locally one-dimensional 600
Difference scheme, monotone 183
Difference scheme, nonconservative 150
Difference scheme, Peaceman — Rachford 548
Difference scheme, predictor-corrector 522
Difference scheme, purely implicit 302
Difference scheme, Richardson 323
Difference scheme, stable 132 306 429
Difference scheme, stable in every harmonic 309
Difference scheme, stable, asymptotically 329
Difference scheme, stable, conditionally 310
Difference scheme, stable, unconditionally 310 334
Difference scheme, stable, with respect to coefficients 230
Difference scheme, three-layer 86 353 445
Difference scheme, truncated 213
Difference scheme, two-layer 302 386
Difference scheme, weighted 301 346 441
Difference, left 2
Difference, right 2
Domain of operator 42
Eigenvalue of an operator 49
Eigenvector of an operator 49
Energy of an operator 44
Energy, identity 318 399 430
Energy, inequality 319
Equation, difference 2
Equation, difference, first-order linear 4 5
Equation, difference, mth-order linear 3
Equation, difference, second-order linear 4 7
Equation, elliptic 237
Equation, heat conduction 300
Equation, hyperbolic 84
Equation, operator 140
Equation, Poisson 237 290
Equation, quasilinear 300
Equation, Schrodinger 349
Equation, stationary 187
Equation, time-dependent 299
Equation, transfer 354
Equation, vibrations 364
Error of the difference approximation 57 69 159
Formulae, "difference differentiation" by parts 29
Formulae, first Green 32
Formulae, second Green 32
Function, difference Green 199
Function, grid 2 51
Function, pattern 208
| grid 2 51 246 248
Grid step 51
Grid, connected 250 259
Grid, equidistant 51
Grid, non-equidistant 52 67
Grid, rectangular 246
Grid, square 246
Harmonic 308
Input data 87
iterations 653
Kronecker's delta 201
Lattice 2
Layer 302
Lipschitz continuity of an operator 420
Majorant 16 262
Maximum principle 15 20 260
Method, alternating direction 711
Method, alternative-triangle 684
Method, Bubnov — Galerkin 221
Method, counter elimination 13
Method, cyclic elimination 37
Method, decomposition 645
Method, energy inequality 113 316 374
Method, factorization 39
Method, integro-interpolation 150 215
Method, left elimination 13
Method, matrix elimination 651
Method, minimal correction 733
Method, minimal residual 733
Method, n-layer composite of period m 618
Method, Newton 517
Method, one-step iterative 653
Method, right elimination 10
Method, Ritz 221
Method, Seidel 676
Method, separation of variables 406
Method, simple iteration 664
Method, steepest descent 734
Method, summator identities 228
Method, test function 150
Method, two-step iterative 653
Method, upper relaxation 678
Model 666
Neighborhood of a node 256
nodes 2 51 245 248
Nodes, adjacent 52
Nodes, boundary 53 246 249 258 703
Nodes, inner 53 246 249 258 703
Nodes, irregular 249 250
Nodes, near-boundary 249 250
Nodes, strictly inner 250
Norm of an operator 42
Operator, "triangular" 457
Operator, additive 42
Operator, adjoint 44
Operator, bounded 42
Operator, commuting 43
Operator, homogeneous 42
Operator, inverse 43
Operator, Laplace 238 280
Operator, linear 42
Operator, resolving 391
Operator, self-adjoint 44
Operator, skew-symmetric 425
Operator, transition 386 391
Operator-difference scheme 384
Pattern 56
Pattern functional 146 147
Pattern, "cross" 241
Pattern, integral 146
Pattern, irregular 67
Primary family 146 156 398
Problem, boundary-value 7 75 82 108 120 136 360
Problem, Cauchy 7 74 75
Problem, eigenvalue 106 108 278
Problem, periodic 496
Problem, stable with respect to the initial data and right-hand side 384
Problem, stationary 507
Problem, Stephan 523
Problem, well-posed 96 232
Range of an operator 42
Regular behaviour 329
Regularization 454
Regularization principle 575
Regularizator 455
Square root of an operator 45
Stability with respect to coefficients 232
Stability with respect to the initial data 389 403
Stability with respect to the right-hand side 389 411
Stability, absolute 389
Stability, asymptotic 329
Stability, strong 232
Temperature wave 514
Theorem, comparison 16 262
Theorem, difference embedding 110 112 281
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