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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 |
Finite element method for boundary-value problems 438 724—740
Finite element method for the diffusion equation 752—759
Finite element method for the Laplace (Poisson) equation 740—752
Finite element method, boundary-value ODEs 438 724—740
Finite element method, boundary-value ODEs, assembly 736 738
Finite element method, boundary-value ODEs, boundary conditions 738—739
Finite element method, boundary-value ODEs, domain discretization 726
Finite element method, boundary-value ODEs, element equations 728 735 737
Finite element method, boundary-value ODEs, functional 727
Finite element method, boundary-value ODEs, Galerkin weighted residual approach 734—739
Finite element method, boundary-value ODEs, interpolating polynomials 726—727 735
Finite element method, boundary-value ODEs, nodal equation 728 731 736 738
Finite element method, boundary-value ODEs, numerical examples 731—732 732—733 739
Finite element method, boundary-value ODEs, Rayleigh — Ritz approach 727—734
Finite element method, boundary-value ODEs, shape functions 726—727 735
Finite element method, boundary-value ODEs, steps in 725—726
Finite element method, boundary-value ODEs, system equation 728
Finite element method, boundary-value ODEs, weighted residual integral 734
Finite element method, boundary-value ODEs, weighting factors 734 735
Finite element method, diffusion equation 752—759
Finite element method, diffusion equation, assembly 756—757
Finite element method, diffusion equation, domain discretization 753
Finite element method, diffusion equation, element equations 756
Finite element method, diffusion equation, Galerkin weighted residual approach 754—758
Finite element method, diffusion equation, interpolating polynomials 753—754
Finite element method, diffusion equation, nodal equations 758
Finite element method, diffusion equation, numerical example 758—759
Finite element method, diffusion equation, shape functions 753—754
Finite element method, diffusion equation, weighted residual integral 754
Finite element method, diffusion equation, weighting factors 755
Finite element method, Galerkin method 721—723
Finite element method, introduction to 711—713
Finite element method, Laplace (Poisson) equation 740—752
Finite element method, Laplace (Poisson) equation, assembly 748—750
Finite element method, Laplace (Poisson) equation, domain discretization 740—742
Finite element method, Laplace (Poisson) equation, element equation 748
Finite element method, Laplace (Poisson) equation, Galerkin weighted residual approach 744—750
Finite element method, Laplace (Poisson) equation, interpolating polynomials 742
Finite element method, Laplace (Poisson) equation, nodal equation 750
Finite element method, Laplace (Poisson) equation, numerical examples 750—752
Finite element method, Laplace (Poisson) equation, shape functions 742—744
Finite element method, Laplace (Poisson) equation, weighted residual integral 744
Finite element method, Laplace (Poisson) equation, weighting factors 746
Finite element method, packages 769
Finite element method, programs for 759—769
Finite element method, Rayleigh — Ritz method 714—719
Finite element method, summary 769—770
First law of thermodynamics 520
Five-point approximation of the Laplace equation 536—543
Fix, G.J. 713
Fixed point 141
Fixed-point iteration 140 141—145
Fixed-point iteration, convergence rate of 144—145
Flannery, B.P. see “Press W.H.”
Flow problems 430—431
Flux-vector-splitting method 690—691
Forcing function 324 503
Forsythe, G.E. 545
FORTRAN 3
Forward substitution 46
Forward-difference, definition of 208
Forward-difference, operator 208
Forward-difference, table 209
Forward-time centered-space method see “FTCS method”
Four-bar linkage 127—129
Four-bar linkage applied problems 185
Fourier components 608
Fourier series 608
Fourier’s law of conduction 330 516 529 571
Fourth-order methods for ODEs, Adams — Bashforth method 383—387
Fourth-order methods for ODEs, Adams — Bashforth — Moulton method 383—388
Fourth-order methods for ODEs, Adams — Moulton method 385—388
Fourth-order methods for ODEs, extrapolated modified midpoint method 378—381
Fourth-order methods for ODEs, Gear method 407
Fourth-order methods for ODEs, Runge — Kutta method 373—376
Fox, R.W 519
Frankel, S.R 549 613
Frequency of oscillation, natural 82 88
Freudenstein, F. 128
Freudenstein’s equation 128
Friction coefficient applied problems 185—186 430—431
Friedrichs, K.O. 662
FTCS method, amplification factor 609
FTCS method, convection number 660
FTCS method, diffusion number 599
FTCS method, finite difference equation 659
FTCS method, hyperbolic PDEs 659—661
FTCS method, modified differential equation 660
FTCS method, multidimensional problems 605
FTCS method, nonlinear PDEs 604
FTCS method, numerical information propagation speed 604
FTCS method, numerical solution 661
FTCS method, parabolic PDEs 599—605
FTCS method, parametric studies 600—605
FTCS method, stability analysis 660
FTCS, acronym 599 659
Fully implicit method 614 678
Function subprogram 3
Functional 714 725
Fundamental function 714
Fundamental function, Rayleigh — Ritz method 714
Fundamental theorem of algebra 156
Galerkin method 438
Galerkin weighted residual approach, FEM for boundary-value ODEs, 734—739
Galerkin weighted residual approach, FEM for boundary-value ODEs, assembly 736
Galerkin weighted residual approach, FEM for boundary-value ODEs, domain discretization 726
Galerkin weighted residual approach, FEM for boundary-value ODEs, element equations 735
Galerkin weighted residual approach, FEM for boundary-value ODEs, examples 731—733
Galerkin weighted residual approach, FEM for boundary-value ODEs, interpolating polynomial 735
Galerkin weighted residual approach, FEM for boundary-value ODEs, nodal equation 736 738
Galerkin weighted residual approach, FEM for boundary-value ODEs, shape functions 735
Galerkin weighted residual approach, FEM for boundary-value ODEs, weighted residual integral 734
Galerkin weighted residual approach, FEM for boundary-value ODEs, weighting factors 734 735
Galerkin weighted residual approach, FEM for diffusion equation 752—759
Galerkin weighted residual approach, FEM for diffusion equation, assembly 756—758
Galerkin weighted residual approach, FEM for diffusion equation, domain discretization 753
Galerkin weighted residual approach, FEM for diffusion equation, element equations 756
Galerkin weighted residual approach, FEM for diffusion equation, examples 758—759
Galerkin weighted residual approach, FEM for diffusion equation, interpolating polynomials 753—754
Galerkin weighted residual approach, FEM for diffusion equation, nodal equation 758
Galerkin weighted residual approach, FEM for diffusion equation, shape functions 753
Galerkin weighted residual approach, FEM for diffusion equation, weighted residual integral 754
Galerkin weighted residual approach, FEM for diffusion equation, weighting factors 755
Galerkin weighted residual approach, FEM for Laplace (Poisson) equation 740—752
Galerkin weighted residual approach, FEM for Laplace (Poisson) equation, assembly 748—756
Galerkin weighted residual approach, FEM for Laplace (Poisson) equation, domain discretization 740—742
Galerkin weighted residual approach, FEM for Laplace (Poisson) equation, element equations 748
Galerkin weighted residual approach, FEM for Laplace (Poisson) equation, examples 750—752
Galerkin weighted residual approach, FEM for Laplace (Poisson) equation, interpolating polynomials 740—744
Galerkin weighted residual approach, FEM for Laplace (Poisson) equation, nodal equation 750
Galerkin weighted residual approach, FEM for Laplace (Poisson) equation, shape functions 742—744
Galerkin weighted residual approach, FEM for Laplace (Poisson) equation, weighted residual integral 744
Galerkin weighted residual approach, FEM for Laplace (Poisson) equation, weighting factors 746
Galerkin weighted residual method, boundary-value ODE 721—723
Galerkin weighted residual method, steps in 721—722
Galerkin weighted residual method, weighted residual integral 722
Galerkin weighted residual method, weighted residuals 721
Galerkin weighted residual method, weighting functions 721
GAMS 7
Gauss elimination see “Systems of linear algebraic equations”
Gauss — Jordan elimination see “Systems of linear algebraic equations”
Gauss — Seidel iteration see “Systems of linear algebraic equations”
Gauss — Seidel method for the Laplace equation 546—548
Gaussian quadrature see “Numerical integration Gaussian
Gear method for stiff ODEs 407—408
Gear, C.W. 402 407
General features of boundary-value ODEs 330—332 439—441
General features of elliptic PDEs 531—532
General features of hyperbolic PDEs 655—657
General features of initial-value ODEs 327—330 340—343
| General features of ODEs 323—325
General features of parabolic PDEs 591—593
General features of PDEs 502—504 516
General linear first-order initial-value ODE 340—341
General linear second-order boundary-value ODE 438 439—140
General nonlinear first-order initial-value ODE 341—342
General nonlinear second-order boundary-value ODE 438 440
General quasilinear first-order nonhomogeneous PDE 504 508
General quasilinear second-order nonhomogeneous PDE 504
General second-order algebraic equation 505
General system of quasilinear first-order nonhomogeneous PDEs 504
Generalized coordinate transformations 566—570
Genereaux equation 186
Genereaux, R.R. 186
Gerald, C.F. 165 222
Given method for eigenvalues 111
Graeff’s root squaring method 169
Gragg, W. 378
Gram — Schmidt process 105
Graphing the solution 130—132
Grid aspect ratio 536 549
Grid lines 596
Grid points 596
Gunn, J.E. 628
Hackbush, W 571
Hadamard, J. 525
Hamilton’s principle 723
Heat conduction see “Heat diffusion”
Heat convection 330
Heat diffusion problem, one-dimensional 444—449 451—454
Heat diffusion problem, one-dimensional, boundary-value ODE 436—437
Heat diffusion problem, one-dimensional, compact three-point fourth-order method 470—471
Heat diffusion problem, one-dimensional, derivative BCs 458—461 462—464
Heat diffusion problem, one-dimensional, equilibrium method 451—454
Heat diffusion problem, one-dimensional, example problem 436—437
Heat diffusion problem, one-dimensional, shooting method 444—449
Heat diffusion problem, two-dimensional 536—543
Heat diffusion problem, two-dimensional, compact fourth-order method 557—561
Heat diffusion problem, two-dimensional, control volume method 571—575
Heat diffusion problem, two-dimensional, derivative BCs 550—552
Heat diffusion problem, two-dimensional, example problem 527—530
Heat diffusion problem, two-dimensional, five-point method 547—548 549—550
Heat diffusion with internal energy generation 552—556
Heat diffusion, Fourier’s law of conduction 330 516 529 571
Heat diffusion, governing equation 512 516—517
Heat diffusion, Laplace (Poisson) equation for 552—556
Heat diffusion, steady one-dimensional 330 436—437
Heat diffusion, steady two-dimensional 516—517 527—530
Heat diffusion, unsteady one-dimensional 519—520 587—589
Heat radiation see “Stefan — Boltzmann equation”
Heat transfer applied problems 429—430 498
Heat transfer coefficient 330
Heat transfer problem see “Heat diffusion problem”
Heat transfer rate 541
Henrici, P.K. 158 169
Hessenberg matrix 111
Heun method 368
High-degree polynomial approximation, cubic splines 221—223
High-degree polynomial approximation, direct fit 197
High-degree polynomial approximation, divided difference 204—205
High-degree polynomial approximation, Lagrange 199
High-degree polynomial approximation, least squares 228—231
High-degree polynomial approximation, Newton-backward-difference 213—214
High-degree polynomial approximation, Newton-forward-difference 211—212
Higher-order boundary-value ODEs 440
Higher-order boundary-value ODEs, solution by superposition 449
Higher-order boundary-value ODEs, solution by the equilibrium method 454—458
Higher-order boundary-value ODEs, solution by the shooting method 449
Higher-order equilibrium methods, boundary-value ODEs 466—471
Higher-order equilibrium methods, boundary-value ODEs, compact three-point fourth-order, method 467—471
Higher-order equilibrium methods, boundary-value ODEs, five-point fourth-order method 467
Higher-order methods for the Laplace (Poisson) equation, compact fourth-order method 557—561
Higher-order methods for the Laplace (Poisson) equation, extrapolation 561—562
Higher-order methods for the Laplace (Poisson) equation, fourth-order centered-difference method 557
Higher-order Newton-Cotes formulas 296—297
Higher-order ODEs, boundary-value 449 454—458
Higher-order ODEs, initial-value 396—397
Higher-order PDEs 503
Hildebrand, F.B 158 169
Hoffman, ID 186 430 521
Homogeneous, ordinary differential equations 324
Homogeneous, partial differential equations 504
Homogeneous, systems of linear algebraic equations 19
Horner’s algorithm 194
Householder method for eigenvalues 111
Householder, A.S. 111 169
Hyett, B.J. 544
Hyperbolic PDEs Chapter 11 651—709
Hyperbolic PDEs, convection equation see “Convection equation”
Hyperbolic PDEs, definition of 505
Hyperbolic PDEs, finite difference method for 657—659
Hyperbolic PDEs, general features of 514—515 655—657
Hyperbolic PDEs, introduction to 651—655
Hyperbolic PDEs, multidimensional problems 682—683
Hyperbolic PDEs, nonlinear equation 682
Hyperbolic PDEs, packages 701
Hyperbolic PDEs, programs for 691—701
Hyperbolic PDEs, summary 701—702
Hyperbolic PDEs, wave equation see “Wave equation”
Hyperspace 505
Hypersurface 505
Identity matrix 23
Ill-conditioned polynomial 157
Ill-conditioned problem 54
Ill-conditioned system of equations 52—55
Implicit Euler method 355—357
Implicit Euler method for stiff ODEs 403—406
Implicit Euler method, comparison with explicit Euler method 357—359
Implicit Euler method, Newton’s method for 356
Implicit Euler method, order 356
Implicit Euler method, stability of 363
Implicit FDE, definition of 350 355
Implicit methods for PDEs, hyperbolic PDEs 657
Implicit methods for PDEs, parabolic PDEs 594 611—623
Implicit numerical diffusion 664—665
Implicit numerical dispersion 664—665
IMSL 7 75 111 169 179 241 413 488
Inconsistent set of equations 19
Increment, in numerical integration 291
Incremental search 130 132
Index notation, dependent variable 596
Index notation, grid point 596
Index notation, independent variable 596
Information propagation speed for hyperbolic PDEs 655
Information propagation speed for parabolic PDEs 594
Information propagation speed, numerical 595 657
Information propagation speed, physical 655 656
Inherited error 351
Initial values for ordinary differential equations 325
Initial values for partial differential equations 524—525
Initial values, initial-value problems see “ODEs initial-value”
Instability, numerical of finite difference approximations of ODEs 361—363
Instability, numerical of finite difference approximations of propagation type PDEs 606—610
Instability, numerical, explicit Euler method 358—359
Integration of polynomials 193
Integration, numerical see “Numerical integration”
Intermediate eigenvalues 95
Interpolating functions for the FEM 725
Interpolating polynomials for the FEM 726—727 735 740—744 753—754
Interpolating polynomials for the FEM, one-dimensional 753—754
Interpolating polynomials for the FEM, two-dimensional 742
Interpolation see “Polynomial approximation”
Interpolation, Bessel centered-difference polynomial 216
Interpolation, cubic splines 221—225
Interpolation, direct fit polynomial 197—198
Interpolation, divided difference polynomial 206—208
Interpolation, inverse 217—218
Interpolation, Lagrange polynomial 198—204
Interpolation, least square 225—234
Interpolation, multivariate polynomials 218—220
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