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Samarskii A.A. — The Theory of Difference Schemes
Samarskii A.A. — The Theory of Difference Schemes

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Название: The Theory of Difference Schemes

Автор: Samarskii A.A.

Аннотация:

The Theory of Difference Schemes emphasizes solutions to boundary value problems through multiple difference schemes. It addresses the construction of approximate numerical methods and computer algorithms for solving mathematical physics problems. The book also develops mathematical models for obtaining desired solutions in minimal time using direct or iterative difference equations. Mathematical Reviews said it is "well-written [and] an excellent book, with a wealth of mathematical material and techniques."


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 786

Добавлена в каталог: 28.11.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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, $\rho$-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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