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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 |
Abramowitz, M. 290 296 303
Absolute error 62
Accelerating convergence of eigenprobleras 99—101
Accuracy 4 62
Accuracy, criterion 62
Accuracy, machine 62
Acoustic wave propagation 514 521—523 684—686
Acoustic wave propagation, exact solution 685—686
Acoustics 521
Acoustics, example problem 652—654
Acronyms, definitions of BC, boundary condition 441
Acronyms, definitions of BTCS, backward-time centered-space 614
Acronyms, definitions of FDA, finite difference approximation 347
Acronyms, definitions of FDE, finite difference equation 350
Acronyms, definitions of FEM, finite element method 724
Acronyms, definitions of FTCS, forward-time centered-space 599 659
Acronyms, definitions of MDE, modified differential equation 544 605
Acronyms, definitions of ODE, ordinary differential equation 323
Acronyms, definitions of PDE, partial differential equation 501
Acton, F.S. 169
Adams methods for ODEs 383
Adams — Bashforth fourth-order FDE 383—384
Adams — Bashforth fourth-order FDE, stability analysis 386—387
Adams — Bashforth methods for ODEs 383
Adams — Bashforth methods for ODEs, coefficients, table of 389
Adams — Bashforth methods for ODEs, stability 389
Adams — Bashforth — Moulton fourth-order method 383—388
Adams — Bashforth — Moulton fourth-order method, example 387
Adams — Bashforth — Moulton fourth-order method, program for 412—413
Adams — Moulton fourth-order FDE 385
Adams — Moulton methods for ODEs 383
Adams — Moulton methods for ODEs, coefficients, table of 390
Adams — Moulton methods for ODEs, stability 390
Adams, J.C. 383
Adaptive integration 299—302
ADI method see “Alternating-direction implicit method”
Adjusted system equation (FEM) 725
AFI method see “Approximate-factorization implicit method”
Aitken’s acceleration method 145
Algebraic equations see “Systems of linear algebraic equations”
Algebraic equations, definition of 129
Alternating-direction implicit (ADI) method, hyperbolic PDEs 683
Alternating-direction implicit (ADI) method, parabolic PDEs 627—628
Amplification factor G for ODEs, definition of 361
Amplification factor G for ODEs, for FDEs 361 363 366 369 374 386—387
Amplification factor G for PDEs, convection equation FDEs 660 662 666 674 676 679
Amplification factor G for PDEs, convection-diffusion equation FDEs 633—636
Amplification factor G for PDEs, definition of 607
Amplification factor G for PDEs, diffusion equation FDEs 609 612 615 620
Amplification factor G for PDEs, wave equation FDEs 688—689
Application subroutine 3
Applied problems, definition of 4
Approach of the book 1
Approximate fits 189—190 225
Approximate Newton’s method 149
Approximate physical boundaries 563
Approximate solution notation, ODEs 347 442
Approximate solution notation, PDEs 534 597 658
Approximate-factorization implicit (AFI) method, hyperbolic PDEs 683
Approximate-factorization implicit (AFI) method, parabolic PDEs 623—629
Approximating functions see “Polynomial approximation”
Approximating polynomials see “Polynomial approximation”
Approximation error 5
Assembling finite element equations, boundary-value problem 736
Assembling finite element equations, diffusion equation 756—758
Assembling finite element equations, Laplace (Poisson) equation 748—750
Associative property of matrices 24
Asymptotic steady-state solution of PDEs 637—639
Auxiliary conditions, ODEs 324 325
Auxiliary conditions, PDEs 524—525
Back substitution 33 35
Backward difference, definition of 208
Backward difference, operator 208
Backward difference, table 209
Backward-time centered-space method see “BTCS method”
Bairstow’s method 164—167
Banded matrix 24
Banded matrix for the five-point method 539
Bashforth, E 383
BASIC 3
Basic Tools of Numerical Analysis, Part I 11—16
BC, acronym 441
BCs see “Boundary conditions”
Beam (laterally loaded) 331 436—437
Beam applied problems 498—499
Bessel centered-difference polynomial 216
Best manner possible fit 189—190 225
Binomial coefficient 212
Binomial coefficient, nonstandard 214
Bisection method see “Interval halving method”
Block tridiagonal matrix 52
Block tridiagonal systems 52
Boundary conditions for ODEs 441
Boundary conditions for PDEs 524—525
Boundary conditions for PDEs, Dirichlet 441 524
Boundary conditions for PDEs, mixed 441 524
Boundary conditions for PDEs, Neumann 441 524
Boundary-value ODEs see “ODEs boundary-value”
Bounding a root 129 130—133
Bracketing methods 129 133 135—140
Brandt, A. 571 580
Brent, R.P. 169
Brent’s method 169
BTCS method, convection equation 677—682
BTCS method, convection-diffusion equation 635—637
BTCS method, diffusion equation 614—619
BTCS, acronym 614
Bulirsch, R. 381
C 3
Calculus of variations 714
Canale, R.P. 222
Cauchy problem 525
Centered difference, definition of 208
Centered difference, operator 208
Centered difference, table 209
Centered-difference formulas for differentiation 260—261 267—268 271
CFL stability criterion see “Courant — Friedrichs — Lewy stability criterion”
Chapra, S.C. 222
Characteristic concepts for hyperbolic PDEs 656—657
Characteristic concepts for parabolic PDEs 593
Characteristic concepts for upwind approximations 658
Characteristic curves see “Characteristic paths”
Characteristic equation see “Characteristic paths”
Characteristic equation in eigenproblems 85 87 88
Characteristic paths for a system of first-order PDEs 509—510
Characteristic paths for first-order PDEs 506 509
Characteristic paths for hyperbolic PDEs 514—515
Characteristic paths for parabolic PDEs 513—514
Characteristic paths for PDEs 505—515
Characteristic paths for second-order PDEs 507—508
Characteristic paths for the convection equation 506 507 509
Characteristic paths for the convection-diffusion equation 523—524
Characteristic paths for the diffusion equation 520
Characteristic paths for the Laplace equation 518
Characteristic paths for the wave equation 522
Characteristic paths, definition of 505—506 526
Chemical reaction applied problem 432—433
Circular pyramid volume applied problem 321
Classification of ODEs 325—326
Classification of PDEs 504—511
Classification of physical problems 326—327 511—516
Closed domain 327 511
Closed domain methods see “Nonlinear equations roots
Colebrook equation applied problem 186
Colebrook, C.F. 186
Collocation method 438 719—721
Collocation method for boundary-value problem 720
Collocation method, numerical example 720—721
Collocation method, steps in 719—720
Column vector 22
| Commutative property of matrices 25
Compact fourth-order approximations, first derivative 468
Compact fourth-order approximations, second derivative 468—469
Compact fourth-order method, boundary-value ODEs 467—471
Compact fourth-order method, PDEs 557—561
Compatibility equation 507
Complementary solution of ODEs 340—341 440
Complex characteristics 511
Complex roots of polynomials 158 162—163
Computational stencils see “Finite difference stencils”
Conditional stability 358
Conformable property of matrices 25
Conic sections 505
Conservation of mass see “Continuity equation”
Consistency for ODE methods, boundary-value ODEs 442 452
Consistency for ODE methods, initial-value ODEs 359—361 365—366 368—369 373 378 384 385
Consistency for PDE methods, elliptic PDEs 544—545
Consistency for PDE methods, hyperbolic PDEs 660 662 666 674 676 679 688
Consistency for PDE methods, parabolic PDEs 605—606 613 615 620 633
Continuity equation 520
Control volume discretization 571—574
Control volume method 571—575
Convection 506
Convection equation 506 521 526 652—653 655—656
Convection equation, characteristic equation for 506
Convection equation, compatibility equation for 506
Convection equation, exact solution of 652—653 656
Convection equation, Numerical examples 661 662—664 667—668 669—670 672 674—675 676—677 680—682
Convection equation, numerical methods, BTCS method 677—682
Convection equation, numerical methods, FTCS method 659—661
Convection equation, numerical methods, Lax method 661—664
Convection equation, numerical methods, Lax — Wendroff one-step method 665—668
Convection equation, numerical methods, Lax — Wendroff two-step method 668—670
Convection equation, numerical methods, MacCormack method 670—673
Convection equation, numerical methods, upwind methods 673—677
Convection equation, programs for 691—701
Convection number, definition of 633 660
Convection of heat 330
Convection, definition of 506
Convection, general features of 506 655—656
Convection-diffusion equation 523—524 526 629—637
Convection-diffusion equation, asymptotic steady-state solution 638—639
Convection-diffusion equation, BTCS method 635—637
Convection-diffusion equation, exact solution of 630—632
Convection-diffusion equation, FTCS method 633—635
Convection-diffusion equation, introduction to 629—632
Convection-diffusion equation, numerical examples 634—635 636—637 638—639
Convection-diffusion equation, numerical methods, asymptotic steady-state solution 637—639
Convection-diffusion equation, numerical methods, BTCS method 635—637
Convection-diffusion equation, numerical methods, FTCS method 633—635
Convergence criteria 547
Convergence rate, fixed-point iteration 144—145
Convergence rate, Newton’s method for roots 147—149
Convergence rate, secant method 152
Convergence, boundary-value ODE methods 450
Convergence, elliptic PDE methods 545
Convergence, hyperbolic PDE methods 662
Convergence, initial-value ODE methods 360 363 364
Convergence, parabolic PDE methods 610—611
Converging solutions of ODEs 351
Courant — Friedrichs — Lewy stability criterion 662
Courant, R. 662
Cramer’s Rule 31—32
Cramer’s rule in characteristic analysis 507
Cramer’s rule in eigenproblems 85—86
Crank — Nicolson method 619—623
Crank — Nicolson method, diffusion equation 619—623
Crank — Nicolson method, system equation for 620
Crank, J. 619
Crout LU factorization method 45
Cubic splines 221—225
Curve fitting see “Polynomial approximation”
Cylindrical coordinates 563
Deflated polynomial 195
Deflation of matrices 111
Deflation of polynomials 159—160 195—196
Deflation technique for eigenvalues 111
Dennis, J.E. 173
Derivative BCs, boundary-value ODEs 458—464
Derivative BCs, elliptic PDEs 550—552
Derivative BCs, finite element method 735 745 754
Derivative BCs, parabolic PDEs 623—625
Derivative function for ODEs 324 338
Descartes’ Rule of Signs 156
Determinants 28—30
Determinants, cofactor of 29
Determinants, definition of 28
Determinants, evaluation by cofactors 29
Determinants, evaluation by diagonal method 28—30
Determinants, evaluation by elimination 43—45
Determinants, minor of 29
Determinants, nonsingular 30
Determinants, singular 30
Deviations (least squares) 225
Diagonal dominance, definition of 24
Diagonal matrix 23
Difference formulas from polynomial differentiation 262—264
Difference formulas from Taylor series 270—271
Difference formulas, introduction to 15
Difference formulas, table of 271
Difference polynomials 208 211—216
Difference polynomials, Bessel centered-difference 216
Difference polynomials, Newton backward-difference 213—215
Difference polynomials, Newton forward-difference 211—213
Difference polynomials, Stirling centered-difference 216
Difference tables 208—211
Difference tables, backward 209
Difference tables, centered 209
Difference tables, definition of 208—209
Difference tables, example of 209
Difference tables, forward 209
Difference tables, polynomial fitting 210—211
Difference tables, round-off errors 210
Differences 208—211
Differences, backward 208
Differences, centered 208
Differences, forward 208
Differential equations, ordinary see “ODEs”
Differential equations, partial see “PDEs”
Differentiation of discrete data 251
Differentiation of polynomials 193 194—195
Differentiation, Numerical see “Numerical differentiation”
Diffusion equation 502 512—513 519—520 526 587—589
Diffusion equation, classification of 519—520
Diffusion equation, derivative BCs 623—626
Diffusion equation, domain of dependence 520 594
Diffusion equation, exact solution of 588—589 592—593
Diffusion equation, example problem 587—589
Diffusion equation, finite element solution of 712—713
Diffusion equation, general features of 592—593
Diffusion equation, implicit methods 613—623
Diffusion equation, introduction to 592—593
Diffusion equation, multidimensional problems 627—629
Diffusion equation, nonlinear equations 625—626
Diffusion equation, numerical examples 600—605 616—618 621—623 625—626 758—759
Diffusion equation, numerical methods, BTCS method 614—619
Diffusion equation, numerical methods, Crank — Nicolson method 619—623
Diffusion equation, numerical methods, derivative BCs 623—625
Diffusion equation, numerical methods, DuFort — Frankel method 613
Diffusion equation, numerical methods, finite element method 752—759
Diffusion equation, numerical methods, FTCS method 599—605
Diffusion equation, numerical methods, Richardson method 611—613
Diffusion equation, range of influence 520 592
Diffusion equation, signal propagation speed 520 593
Diffusion number, definition of 599 633
Diffusion of heat 330
Diffusion, numerical see “Implicit numerical diffusion”
Diffusion, physical 592
Dirac delta function 721
Direct elimination methods see “System of linear algebraic equations”
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