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| Ïîèñê ïî óêàçàòåëÿì |
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| Hoffman J.D. — Numerical Methods for Engineers and Scientists |
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| Ïðåäìåòíûé óêàçàòåëü |
Southwell’s relaxation method 64—65
Space marching initial-value problem 327 343
Spacelike coordinate 512—513
Sparse matrix 24
Specific heat of air 228 230
Speed of propagation 510
Speed of propagation for the convection equation 506
Speed of propagation for the diffusion equation 520
Speed of propagation for the wave equation 522
Spherical coordinates 563
SPLINE 221
Spring-mass system, dynamic 87—88
Spring-mass system, static 18—19
Square matrix 23
Stability analysis of ODEs 360—364
Stability analysis of ODEs, amplification factor G 361
Stability analysis of ODEs, conditional stability 359
Stability analysis of ODEs, definition of 360
Stability analysis of ODEs, explicit Euler method 363
Stability analysis of ODEs, fourth-order Adams — Bashforth method 386—387
Stability analysis of ODEs, fourth-order Runge — Kutta method 374
Stability analysis of ODEs, implicit Euler method 363
Stability analysis of ODEs, linear ODEs 362
Stability analysis of ODEs, model equation 362
Stability analysis of ODEs, modified Euler method 366
Stability analysis of ODEs, nonlinear ODEs 361—362
Stability analysis of ODEs, procedure 362
Stability analysis of ODEs, stable FDE 361
Stability analysis of ODEs, summary 364
Stability analysis of ODEs, unconditional stability 359
Stability analysis of ODEs, unstable FDE 361
Stability analysis of PDEs, discrete perturbation method 607
Stability analysis of PDEs, matrix method 607
Stability analysis of PDEs, von Neumann method 607—610
Stability analysis of PDEs, von Neumann method, amplification factor G 607
Stability analysis of PDEs, von Neumann method, convection equation, BTCS method 679
Stability analysis of PDEs, von Neumann method, convection equation, BTCS method, FTCS method 660
Stability analysis of PDEs, von Neumann method, convection equation, BTCS method, Lax method 662
Stability analysis of PDEs, von Neumann method, convection equation, BTCS method, Lax — Wendroff one-step method 666—667
Stability analysis of PDEs, von Neumann method, convection equation, BTCS method, upwind (first-order) method 674
Stability analysis of PDEs, von Neumann method, convection equation, BTCS method, upwind (second-order) method 676
Stability analysis of PDEs, von Neumann method, convection-diffusion equation, BTCS method 636
Stability analysis of PDEs, von Neumann method, convection-diffusion equation, FTCS method 633—634
Stability analysis of PDEs, von Neumann method, diffusion equation, BTCS method 615
Stability analysis of PDEs, von Neumann method, diffusion equation, Crank — Nicolson method 620
Stability analysis of PDEs, von Neumann method, diffusion equation, DuFort — Frankel method 613
Stability analysis of PDEs, von Neumann method, diffusion equation, FTCS method 609—610
Stability analysis of PDEs, von Neumann method, diffusion equation, Richardson method 612
Stability analysis of PDEs, von Neumann method, Fourier components 608
Stability analysis of PDEs, von Neumann method, nonlinear instabilities 607
Stability analysis of PDEs, von Neumann method, procedure 608
Stability analysis of PDEs, von Neumann method, wave equation, Lax — Wendroff one-step method 688—689
Stable ODE, definition of 341 351
Stefan — Boltzmann constant 327 430
Stefan — Boltzmann law of radiation 327
Steffensen’s method 145
Stegun, I.A. 290 296 303
Stencils see “Finite difference stencils”
Step size control 376—378 390—391
Stewart, G.W. 111
Stiff initial-value ODEs 400—408
Stiff initial-value ODEs, definition of stiffness 400—401
Stiff initial-value ODEs, explicit Euler method 403—404
Stiff initial-value ODEs, Gear method 407—408
Stiff initial-value ODEs, higher-order implicit methods 407—408
Stiff initial-value ODEs, implicit Euler method 403 405—406
Stiff initial-value ODEs, model ODE 402—403
Stiff initial-value ODEs, single first-order ODE 401—406
Stiff initial-value ODEs, stiffness ratio 406
Stiff initial-value ODEs, systems of first-order ODEs 406—407
Stirling centered-difference polynomial 216
Stoer, J. 381
Straight line approximation, least squares 227—228
Strang, G 104 111
Substantial derivative 521
Successive univariate interpolation 218—220
Successive univariate polynomials 218—220
Successive-over-relaxation see “System of linear algebraic equations SOR”
Summation convention 28
Superposition of linear boundary-value ODE solutions 447—448
Symmetric matrix 24
Synthetic division algorithm for polynomials 195—196
System condition 54—55
System equation for BTCS method 546 616 680
System equation for Crank — Nicolson method 620—621
System equation for eigenproblems 83
System equation for finite element methods 724 728
Systems of first-order initial-value ODEs 343
Systems of linear algebraic equation, numerical methods, Cramer’s rule 31—32
Systems of linear algebraic equation, numerical methods, Crout LU factorization 45
Systems of linear algebraic equation, numerical methods, direct elimination methods 20 30—45
Systems of linear algebraic equation, numerical methods, Doolittle LU factorization 45—48
Systems of linear algebraic equation, numerical methods, elimination methods 32—39
Systems of linear algebraic equation, numerical methods, Gauss — Jordan elimination 41—42
Systems of linear algebraic equation, numerical methods, Gauss — Jordan elimination for finding matrix inverse 42
Systems of linear algebraic equation, numerical methods, Gauss — Jordan elimination for solving linear systems 41—42
Systems of linear algebraic equation, numerical methods, Gauss — Seidel method 63—64
Systems of linear algebraic equation, numerical methods, Gauss-elimination 39—40
Systems of linear algebraic equation, numerical methods, iterative methods 20 59—67
Systems of linear algebraic equation, numerical methods, Jacobi method 59—61
Systems of linear algebraic equation, numerical methods, LU factorization 45—48
Systems of linear algebraic equation, numerical methods, matrix inverse method 43
Systems of linear algebraic equation, numerical methods, matrix inversion 42
Systems of linear algebraic equation, numerical methods, multiple b vectors 36
Systems of linear algebraic equation, numerical methods, operation counts 40 41 43 47 51 542—543
Systems of linear algebraic equation, numerical methods, relaxation (Southwell) 64—65
Systems of linear algebraic equation, simple elimination 35
Systems of linear algebraic equation, successive-over-relaxation (SOR) 64—67 548—550
Systems of linear algebraic equation, successive-over-relaxation (SOR), optimum over-relaxation factor 67 549
Systems of linear algebraic equation, successive-over-relaxation (SOR), over-relaxation factor 65—67 548—549
Systems of linear algebraic equation, Thomas algorithm 49—52
Systems of linear algebraic equation, tridiagonal systems 49—52
Systems of linear algebraic equation, tridiagonal systems, block tridiagonal systems 52
Systems of linear algebraic equation, tridiagonal systems, definition of 49
Systems of linear algebraic equation, tridiagonal systems, LU factorization 51
Systems of linear algebraic equation, tridiagonal systems, Thomas algorithm 49—51
Systems of linear algebraic equations Chapter 1 17—80
Systems of linear algebraic equations, accuracy 61—62
Systems of linear algebraic equations, back substitution 32—33
Systems of linear algebraic equations, block tridiagonal system 52
Systems of linear algebraic equations, consistent system 19
Systems of linear algebraic equations, convergence 62—63
Systems of linear algebraic equations, definition of 19
Systems of linear algebraic equations, diagonal dominance 59
Systems of linear algebraic equations, direct elimination methods 20 30—52
Systems of linear algebraic equations, elimination 32—35
Systems of linear algebraic equations, elimination methods 32—39
Systems of linear algebraic equations, errors 62
Systems of linear algebraic equations, example 18—19
Systems of linear algebraic equations, Gauss elimination 39—40
Systems of linear algebraic equations, Gauss — Jordan elimination 41—42
Systems of linear algebraic equations, Gauss — Jordan elimination for matrix inverse 42
Systems of linear algebraic equations, Gauss — Seidel iteration 63—64
Systems of linear algebraic equations, homogeneous system 19
Systems of linear algebraic equations, homogeneous system in eigenproblems 84—86
Systems of linear algebraic equations, ill-conditioned systems 52—59
Systems of linear algebraic equations, inconsistent system 19
Systems of linear algebraic equations, introduction to 11 18—21
Systems of linear algebraic equations, iterative methods 20 59—67
Systems of linear algebraic equations, Jacobi method 59—61
Systems of linear algebraic equations, matrix notation for 27
Systems of linear algebraic equations, methods of solution 20
Systems of linear algebraic equations, methods of solution, direct elimination 20
Systems of linear algebraic equations, methods of solution, iterative 20
Systems of linear algebraic equations, multiple b vectors 36
Systems of linear algebraic equations, numerical examples 31—32 34—35 35 36 37 38—39 41—42 42 43 44—45 46—47 48 50—51 52—54 54—55 57—58 60—61 64 66
Systems of linear algebraic equations, pivoting 36—37
Systems of linear algebraic equations, programs for 67—75
Systems of linear algebraic equations, redundant system 19
Systems of linear algebraic equations, relaxation (Southwell) 64
| Systems of linear algebraic equations, residual 60 63 65
Systems of linear algebraic equations, row operation 28
Systems of linear algebraic equations, scaled pivoting 37—39
Systems of linear algebraic equations, scaling 37—39
Systems of linear algebraic equations, simple elimination 35
Systems of linear algebraic equations, solution possibilities 19
Systems of linear algebraic equations, SOR see “Successive-over-relaxation”
Systems of linear algebraic equations, successive-over-relaxation 64—67
Systems of linear algebraic equations, summary 76—77
Systems of linear algebraic equations, trivial solution 19
Systems of linear algebraic equations, unique solution 19
Systems of nonlinear equations 169—173
Systems of nonlinear equations, multidimensional minimization 173
Systems of nonlinear equations, Newton’s method 170—173
Systems of ordinary differential equations (ODEs) 325
Systems of partial differential equations (PDEs) 504
Systems of second-order boundary-value ODEs 441
Tangent method 146
Taylor formula 8 535
Taylor polynomial 7 8 34 182
Taylor polynomial, remainder term 348
Taylor polynomial, truncation error 348
Taylor series 7 192
Taylor series in consistency analysis 349
Taylor series method for ODEs 353—346
Taylor series, difference formulas from 264—270
Taylor series, one independent variable 8
Taylor series, remainder term 8
Taylor series, two-independent variables 9
Taylor, R.L. 713
Temperature gradient applied problem 284
Teukolsky, S.A. see “Press W.H.”
Thermal diffusivity 519
Thomas algorithm 49—52
Thomas, L.H. 49
Thompson, J.F. 570
Three-dimensional problems for elliptic PDEs 571
Time linearization, boundary-value ODEs 393—394
Time linearization, nonlinear parabolic PDEs 626—627
Time marching initial-value ODEs 327 343
Timelike coordinate 327 343 513
Timelike direction 327 512
Timoshenko, S. 331
Transcendental equations 129
Transformation metrics 569
Transformed spaces 563 566 568—570
Transpose matrix 24
Trapezoid method for ODEs 364 368
Trapezoid Rule see “Numerical integration”
Trial functions, collocation method 719
Trial functions, finite element method 724
Trial functions, Galerkin weighted residual method 721
Trial functions, Rayleigh —Ritz method 716
Triangular elements, FEM 740—741
Triangular matrix 23
Triangular matrix, lower triangular 23
Triangular matrix, upper triangular 23
Tridiagonal matrices 24 49—52
Tridiagonal matrices, block tridiagonal 52
Tridiagonal system of equations 49—51
Tridiagonal system of equations, block tridiagonal 52
Tridiagonal system of equations, definition of 49
Tridiagonal system of equations, LU factorization 51
Tridiagonal system of equations, numerical example 50—51
Tridiagonal system of equations, Thomas algorithm 49—52
Trivial solution 19
Truncation error of difference formulas 267
Truncation error of ODE approximations 351
Truncation error of PDE approximations 535
Truncation error of Taylor polynomial 348
Truncation error, definition of 351
Unconditional stability 359
Unconditional stability, BTCS method 616 679
Unconditional stability, Crank — Nicolson method 620
Unconditional stability, implicit Euler method 357—359
Undamped natural frequency 82
Under-relaxation 65
Unequally spaced data, differentiation of 254—257
Unequally spaced data, fitting polynomials to 197—208
Unequally spaced data, integration of 288—289 292
Unequally spaced data, interpolation of 197—208
Unique solution of a linear system 19—20
Uniqueness theorem for polynomials 192
Unit vector 22
Unstable ODE, definition of 341 351
Upper triangular matrix 23
Upwind methods 673—677
Upwind methods, first-order upwind method 673—675
Upwind methods, first-order upwind method, amplification factor G 674
Upwind methods, first-order upwind method, finite difference equation 673
Upwind methods, first-order upwind method, finite difference stencil 673
Upwind methods, first-order upwind method, modified differential equation 673
Upwind methods, first-order upwind method, numerical example 674—675
Upwind methods, first-order upwind method, second-order upwind method 675—677
Upwind methods, first-order upwind method, stability analysis 676
van der Waal equation applied problem 185
Variable grid spacing see “Nonuniform grids”
Variable-area channel applied problems 186 430—431
Variable-area passage applied problems 186 430—431
Variation, calculus of variations 715
Vectors, column vector 22
Vectors, definition of 22
Vectors, orthogonal vectors 22
Vectors, row vector 22
Vectors, unit vector 22
Velocity distribution applied problem 498
Velocity gradient applied problem 283
Vetterling, W.T. see “Press W.H.”
Vibrating masses 81—83
Vibration of a machine applied problem 431
von Neumann method see “Stability analysis von
Warming, R.F. 544
Warsi, Z.U.A. 570
Wasow, W 545
Wave equation 502 520—523 526 683—691
Wave equation, auxiliary conditions 683
Wave equation, characteristics concepts 686—687
Wave equation, classification of 522
Wave equation, coupled convection equations 523 685
Wave equation, derivation of 520—522
Wave equation, d’Alembert solution of 684
Wave equation, example problem 684—686
Wave equation, general features of 683—686
Wave equation, introduction to 502 520—523 653 683—686
Wave equation, numerical example 689—690
Wave equation, numerical methods, flux-vector-splitting methods 690—691
Wave equation, numerical methods, Lax — Wendroff one-step method 687—690
Wave equation, numerical methods, Lax — Wendroff one-step method, amplification matrix G 688
Wave equation, numerical methods, Lax — Wendroff one-step method, finite difference equations 688
Wave equation, numerical methods, Lax — Wendroff one-step method, modified differential equation (MDE) 688
Wave equation, numerical methods, Lax — Wendroff one-step method, numerical example 689—690
Wave equation, numerical methods, Lax — Wendroff one-step method, stability analysis 688—689
wave number 608
Wave propagation speed 653
Wavelines 657
Weierstrass approximation theorem 191
Weighted residual integral 725 734 744 754
Weighted residual integral, boundary-value ODE 722 734
Weighted residual integral, diffusion equation 754
Weighted residual integral, Laplace (Poisson) equation 754
Weighted residuals 721
Weighting factors (functions) 721
Weighting factors (functions), boundary-value problems 722 735
Weighting factors (functions), diffusion equation 755
Weighting factors (functions), Laplace equation 746
Weighting factors for FEM 734 746 755
Well-conditioned problem 54
Well-posed problems 525
Wendroff, B. 665 668 687
Wheatley, P.O. 165 222
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