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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 |
Direct fit multivariate polynomials 220
Direct fit polynomials 197—198
Direct fit polynomials, differentiation of 255—257
Direct fit polynomials, error of 198
Direct fit polynomials, fitting 197—198
Direct fit polynomials, integration of 288—289
Direct fit polynomials, interpolation with 197—198
Direct fit polynomials, programs for 235—236
Direct method for eigenvalues 101—104
Direct methods for systems of linear algebraic equations see “Systems of linear algebraic equations”
Direct power method for eigenvalues 90—91
Dirichlet BCs, ODEs 441
Dirichlet BCs, PDEs 524
Discrete perturbation stability analysis 607
Discriminant of conic sections 505
Discriminant of PDEs 505
Discriminant of the convection-diffusion equation 523
Discriminant of the diffusion equation 519
Discriminant of the Laplace equation 517
Discriminant of the wave equation 522
Discriminant of two coupled convection equations 510
Dispersion, numerical see “Implicit numerical dispersion”
Dissipation function 503
Distributive property of matrices 26
Diverging solution of ODEs 351
Divided difference 204
Divided difference polynomials 206—208
Divided difference polynomials, differentiation of 255—257
Divided difference polynomials, error of 207—208
Divided difference polynomials, fitting 206
Divided difference polynomials, interpolation with 207—208
Divided difference polynomials, program for 238
Divided difference, definition of 204
Divided difference, operator 204
Divided difference, table 204—206
Division algorithm for polynomials 194
Domain discretization for the finite element method, one-dimensional 726 753
Domain discretization for the finite element method, two-dimensional 740—742
Domain of dependence of differential equations, convection equation 506
Domain of dependence of differential equations, definition of 508
Domain of dependence of differential equations, diffusion equation 520
Domain of dependence of differential equations, elliptic PDEs 508 512 518 531
Domain of dependence of differential equations, hyperbolic PDEs 508 528 655 657
Domain of dependence of differential equations, Laplace equation 518
Domain of dependence of differential equations, parabolic PDEs 508 520 592 593
Domain of dependence of differential equations, wave equation 523
Domain of dependence, numerical of explicit methods 595 657
Domain of dependence, numerical of implicit methods 595
Domains, closed for ODEs 327
Domains, closed for PDEs 511
Domains, open for ODEs 327
Domains, open for PDEs 512
Doolittle LU factorization method 45—48
Doolittle LU factorization method for matrix inverse 48
Doolittle LU factorization method in eigenproblems 93—95
DOUBLE PRECISION 5
Douglas, J. 618 627 628
Drag coefficient 329
DuFort — Frankel method 613
DuFort, E.C. 613
d’Alembert solution of the wave equation 683—684
Eigenproblems chapter 2 81—125
Eigenproblems for boundary-value ODEs 327 480—482
Eigenproblems for boundary-value ODEs, approximate eigenvalues 481—482
Eigenproblems for boundary-value ODEs, exact eigenvalues 480—481
Eigenproblems in PDEs 515—516
Eigenproblems, basic characteristics of 81—85
Eigenproblems, basis of power method 91—92
Eigenproblems, Boundary-value ODEs 480—482
Eigenproblems, Boundary-value ODEs, approximate eigenvalues 481—482
Eigenproblems, Boundary-value ODEs, exact eigenvalues 480—481
Eigenproblems, Boundary-value ODEs, example 481—482
Eigenproblems, characteristic equation for 87 88
Eigenproblems, classical form 87
Eigenproblems, Cramer’s rule 85—86
Eigenproblems, definition of 83—84
Eigenproblems, deflation techniques 111
Eigenproblems, direct method 101—104
Eigenproblems, direct method, linear eigenproblems 102—103
Eigenproblems, direct method, nonlinear eigenproblems 103—104
Eigenproblems, direct power method 90—91
Eigenproblems, Doolittle LU method for inverse power method 93
Eigenproblems, example of 81—84
Eigenproblems, illustration of 84—85
Eigenproblems, introduction to 81—85
Eigenproblems, inverse power method 92—95
Eigenproblems, largest eigenvalue 90—92
Eigenproblems, mathematical characteristics of 85—89
Eigenproblems, nonlinear eigenproblems 101—104
Eigenproblems, Numerical examples 90—91 94—104 107—109 110—111
Eigenproblems, other methods 111
Eigenproblems, packages 118
Eigenproblems, PDEs 514—515
Eigenproblems, power method 89—104
Eigenproblems, programs for 112—118
Eigenproblems, programs for direct power method 112—114
Eigenproblems, programs for inverse power method 115—118
Eigenproblems, QR method 104—109
Eigenproblems, shifting eigenvalues 95—101
Eigenproblems, shifting eigenvalues for intermediate eigenvalues 97—99
Eigenproblems, shifting eigenvalues for opposite extreme eigenvalues 95—97
Eigenproblems, shifting eigenvalues to accelerate convergence 99—101
Eigenproblems, smallest eigenvalue 95—96
Eigenproblems, summary 101
Eigenproblems, unity component 90 92
Eigenvalues see “Eigenproblems”
Eigenvalues of ODEs 327 480—482
Eigenvalues of ODEs, approximate 481—482
Eigenvalues of ODEs, exact 480—481
Eigenvalues, characteristic equation for 87 88
Eigenvalues, definition of 13 83 84 87
Eigenvalues, example of 81—84 84—85
Eigenvectors, definition of 13 83 84 88
Eigenvectors, determination of 88 110—111
Eigenvectors, unity component of 90 92 110
EISPACK 111 118
Electric circuit applied problems 431—432
Element equations, FEM 724 735 748 756
Element equations, FEM, boundary-value ODEs 737
Element equations, FEM, diffusion equation 756
Element equations, FEM, Laplace (Poisson) equation 748
Elementary row operations 32
Elements, FEM 724
Elements, FEM, one-dimensional 724—725
Elements, FEM, rectangular 740—741
Elements, FEM, trapezoidal 740—741
Elements, FEM, triangular 740—741
Elimination 32—39
Elimination methods see “Systems of linear algebraic equations”
Elliptic PDEs see “Laplace (Poisson) equation”
Elliptic PDEs, consistency 544—545
Elliptic PDEs, convergence 545—546
Elliptic PDEs, definition of 505
Elliptic PDEs, Laplace equation 516
Elliptic PDEs, multidimensional problems 571
Elliptic PDEs, nonlinear equations 570—571
Elliptic PDEs, packages 580
Elliptic PDEs, Poisson equation 518
Elliptic PDEs, programs for 575—580
Elliptic PDEs, summary 580—581
Elliptic PDEs, the finite difference method for 532—536
energy equation 520
Equally spaced data, differentiation of 257—264
Equally spaced data, fitting polynomials to 208—216
Equally spaced data, integration of 290—299
Equally spaced data, interpolation of 208—216
Equations, algebraic see “Systems of linear algebraic equations”
Equations, Colebrook 186
Equations, convection 526 652—653 655—656
Equations, convection-diffusion 523—524 526 629—637
| Equations, diffusion 512—514 519—520 524 587—591 599—626
Equations, Fourier’s law of conduction 330 516 529 571
Equations, Laplace 502 516—518 526 528 530 536—552
Equations, least squares normal 227 229 232
Equations, linear see “Systems of linear algebraic equations”
Equations, Newton’s law of cooling 330
Equations, Poisson 503 518 530 552—557
Equations, Stefan — Boltzmann law of radiation 328
Equations, van der Waal 185
Equations, wave 653 683—691
Equilibrium method for boundary-value ODEs 438 450—458
Equilibrium method for boundary-value ODEs, advantages of 489
Equilibrium method for boundary-value ODEs, derivative BCs 461—464
Equilibrium method for boundary-value ODEs, disadvantages of 489
Equilibrium method for boundary-value ODEs, extrapolation 453—454
Equilibrium method for boundary-value ODEs, higher-order ODEs 466—471
Equilibrium method for boundary-value ODEs, nonlinear problems, iteration 471—474
Equilibrium method for boundary-value ODEs, nonlinear problems, Newton’s method 474—477
Equilibrium method for boundary-value ODEs, second-order ODE 450—453
Equilibrium problems, ODEs 326—327 437
Equilibrium problems, PDEs 511—512 516—519
Equivalence theorem for ODEs 363
Equivalence theorem for PDEs 610
Error control for ODEs see “Error estimation for ODE methods”
Error estimation for numerical approximations for difference formulas 272
Error estimation for numerical approximations of numerical algorithms 270 272
Error estimation for ODE methods, fourth-order Adams — Bashforth — Moulton method 390—391
Error estimation for ODE methods, multipoint methods 390—391
Error estimation for ODE methods, Runge — Kutta — Fehlberg method 377—378
Error estimation for ODE methods, single-point methods 376
Error propagation 351—352
Error term, polynomial 192
Error term, Taylor polynomial 8 192
Errors 5 62
Errors in the solution of ODEs 351—352
Errors in the solution of ODEs, absolute error 62
Errors in the solution of ODEs, algebraic errors 351
Errors in the solution of ODEs, global 292 294 296
Errors in the solution of ODEs, inherited error 352
Errors in the solution of ODEs, initial data errors 351
Errors in the solution of ODEs, local 292 294 296 297
Errors in the solution of ODEs, relative error 62
Errors in the solution of ODEs, round-off error 352
Errors in the solution of ODEs, truncation error 351
Errors, absolute 62
Errors, approximation 5
Errors, iteration 5
Errors, relative 62
Errors, round-off 5
Euclidean norm of a matrix 56
Euclidean norm of a vector 56
Euclidean norm of errors in ODE solutions 446—447
Euler equation in calculus of variations 714
Euler’s explicit method see “Explicit Euler method”
Euler’s implicit method see “Implicit Euler method”
Euler’s modified method see “Modified Euler method”
Evaluation of polynomials 194—198
Exact fits 189—190
Exact solution notation 347 442 534 597 658
Exact solutions, boundary-value ODEs 436—437
Exact solutions, convection equation 652—653 656
Exact solutions, convection-diffusion equation 630—632
Exact solutions, diffusion equation 587—589
Exact solutions, initial-value ODEs 336 398
Exact solutions, Laplace equation 528—530
Exact solutions, linear first-order ODE 340—341
Exact solutions, linear second-order ODE 440
Exact solutions, Poisson equation 553—554
Excel 6 75
Exercise problems, definition of 4
Explicit Euler method 352—355
Explicit Euler method as predictor 368—370
Explicit Euler method for stiff ODEs 403—404
Explicit Euler method, comparison with implicit Euler method 357—359
Explicit Euler method, consistency 360—361
Explicit Euler method, convergence 363
Explicit Euler method, order 353 361
Explicit Euler method, stability of 363
Explicit method, definition of 350 355
Explicit methods, hyperbolic PDEs 657
Explicit methods, initial-value ODEs 350
Explicit methods, parabolic PDEs 594
Extrapolated modified midpoint method 378—381
Extrapolated modified midpoint method, Bulirsch — Stoer method 381
Extrapolated modified midpoint method, comparison with Runge — Kutta method 380—381
Extrapolated modified midpoint method, concept 378
Extrapolated modified midpoint method, program for 410—412
Extrapolation of boundary-value ODE solutions 448—449
Extrapolation of difference formulas 272
Extrapolation of initial-value ODE solutions 378—381
Extrapolation of integration formulas 297—299
Extrapolation of Laplace equation solutions 561—562
Extrapolation of numerical algorithms 270 272
Extremization 714
Factor theorem for polynomials 194
Fadeev, D.K. 111
Fadeeva, YN. 111
False position method 135 138—140
FDA, acronym 347
FDE, acronym 350
Fehlberg method see “Runge — Kutta — Fehlberg method”
Fehlberg, E. 377
FEM, acronym 724
Ferziger, J.H. 628
Finite difference approximations for boundary-value ODEs 450—451
Finite difference approximations for elliptic PDEs 534—536
Finite difference approximations for hyperbolic PDEs 658—659
Finite difference approximations for initial-value ODEs 347—349
Finite difference approximations for parabolic PDEs 597—598
Finite difference equations, elliptic PDEs 536
Finite difference equations, explicit 350
Finite difference equations, hyperbolic PDEs 658—659
Finite difference equations, implicit 350
Finite difference equations, introduction to ODEs 349—350
Finite difference equations, parabolic PDEs 599
Finite difference grids for boundary-value ODEs 450—451
Finite difference grids for elliptic PDEs 533—534
Finite difference grids for hyperbolic PDEs 658
Finite difference grids for initial-value ODEs 346—347
Finite difference grids for parabolic PDEs 596
Finite difference method for ODEs, approximate solution 348
Finite difference method for ODEs, exact solution 347
Finite difference method for ODEs, finite difference approximations 347—349
Finite difference method for ODEs, finite difference equations 349—350
Finite difference method for ODEs, finite difference grids 346—347
Finite difference method for PDEs, elliptic PDEs 532—536
Finite difference method for PDEs, hyperbolic PDEs 657—659
Finite difference method for PDEs, parabolic PDEs 593—599
Finite difference stencil, definition of 537
Finite difference stencils, convection equation, BTCS FDE 678
Finite difference stencils, convection equation, FTCS FDE 660
Finite difference stencils, convection equation, Lax FDE 662
Finite difference stencils, convection equation, Lax — Wendroff one-step FDE 666
Finite difference stencils, convection equation, Lax — Wendroff two-step FDEs 669
Finite difference stencils, convection equation, MacCormack FDEs 672
Finite difference stencils, convection equation, upwind (first order) FDE 673
Finite difference stencils, convection equation, upwind (second-order) FDE 676
Finite difference stencils, convection-diffusion equation, BTCS FDE 635
Finite difference stencils, convection-diffusion equation, FTCS FDE 633
Finite difference stencils, diffusion equation, BTCS FDE 614
Finite difference stencils, diffusion equation, Crank — Nicolson FDE 620
Finite difference stencils, diffusion equation, derivative BC 624
Finite difference stencils, diffusion equation, FTCS FDE 599
Finite difference stencils, diffusion equation, Richardson FDE 611
Finite difference stencils, Laplace (Poisson) equation, compact fourth-order FDE 559
Finite difference stencils, Laplace (Poisson) equation, control volume method 574
Finite difference stencils, Laplace (Poisson) equation, derivative BC 552
Finite difference stencils, Laplace (Poisson) equation, five-point FDE 537
Finite difference stencils, Laplace (Poisson) equation, nonuniform grid 564
Finite element method Chapter 12 711—773
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