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| Àâòîðèçàöèÿ |
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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 |
Polynomial approximation, inverse interpolation 217—218
Polynomial approximation, Lagrange polynomials 198—204
Polynomial approximation, least squares polynomials (see also “Least squares approximation”) 225—234 (see also “Least squares approximation”)
Polynomial approximation, multivariate polynomials 218—220
Polynomial approximation, Neville’s algorithm 201—204
Polynomial approximation, Newton backward-difference polynomials 211—213
Polynomial approximation, Newton forward-difference polynomials 213—215
Polynomial approximation, numerical examples 197—198 200—201 203—204 207—208 212—213 214—215 217—218 219—220 220 223—225 227—228 230—231 232—233
Polynomial approximation, programs for 235—241
Polynomial approximation, properties of polynomials see “Polynomials properties
Polynomial approximation, Stirling polynomial 216
Polynomial approximation, successive univariate polynomials 218—220
Polynomial approximation, summary 242—243
Polynomial deflation 195—196
Polynomial interpolation see “Polynomial approximation”
Polynomial roots of 155—167
Polynomial roots of, Bairstow’s method 164—167
Polynomial roots of, Descartes’ rule of signs 156—157
Polynomial roots of, ill-conditioned polynomials 157
Polynomial roots of, introduction to 155—158
Polynomial roots of, Newton’s method for complex roots 162—163
Polynomial roots of, Newton’s method for multiple roots 160—162
Polynomial roots of, Newton’s method for multiple roots, basic method 160
Polynomial roots of, Newton’s method for multiple roots, modified function method 160
Polynomial roots of, Newton’s method for multiple roots, multiplicity method 160
Polynomial roots of, Newton’s method for simple roots 158—163
Polynomial roots of, polynomial deflation 159—160
Polynomial roots of, quadratic formula 156
Polynomial roots of, rationalized quadratic formula 156
Polynomial roots of, root polishing 157
Polynomial roots of, summary 167
Polynomials, properties of 190—196
Polynomials, properties of, deflation 195—196
Polynomials, properties of, differentiation of 193 194—195
Polynomials, properties of, division algorithm 194
Polynomials, properties of, error term 192
Polynomials, properties of, evaluation of 194—196
Polynomials, properties of, factor theorem 194
Polynomials, properties of, general form of 190
Polynomials, properties of, Horner’s algorithm 194
Polynomials, properties of, integration of 193
Polynomials, properties of, nested multiplication 194 195—196
Polynomials, properties of, remainder theorem 194
Polynomials, properties of, synthetic division 195—196
Polynomials, properties of, Taylor polynomial 192
Polynomials, properties of, Taylor polynomial, remainder term 192
Population growth applied problems 429 432
Power method see “Eigenproblems power
Power method, basis of 91—92
Power method, direct power method 90—91
Power method, inverse power method 92—95
Power method, shifted power method 95—101
Power series 7—8
PRECISION 4
Precision, double 5
Precision, quad 5
Precision, single 5
Predictor-corrector methods for ODEs, Adams — Bashforth — Moulton method 383—388
Predictor-corrector methods for ODEs, modified Euler method 368—370
Press, W.H. 7 75 111 169 179 222 242 279 315 413 488
Program, main 3
Programming languages 3
Programs, boundary-value ODEs 483—488
Programs, boundary-value ODEs, fourth-order Runge — Kutta shooting method 483—486
Programs, boundary-value ODEs, second-order equilibrium method 486—488
Programs, convection equation 691—701
Programs, convection equation, BTCS method 699—701
Programs, convection equation, Lax method 692—694
Programs, convection equation, Lax — Wendroff one-step method 694—695
Programs, convection equation, MacCormack method 695—697
Programs, convection equation, upwind method 697—699
Programs, eigenvalues 112—118
Programs, eigenvalues, direct power method 112—114
Programs, eigenvalues, inverse power method 115—118
Programs, finite element method 759—769
Programs, finite element method, boundary-value ODEs 760—763
Programs, finite element method, diffusion equation 766—769
Programs, finite element method, Laplace (Poisson) equation 763—766
Programs, general philosophy of 3
Programs, initial-value ODEs 408—413
Programs, initial-value ODEs, extrapolated modified midpoint method 410—412
Programs, initial-value ODEs, fourth-order Adams — Bashforth — Moulton method 412—413
Programs, initial-value ODEs, fourth-order Runge — Kutta method 408—410
Programs, Laplace (Poisson) equation 575—580
Programs, Laplace (Poisson) equation, five-point method Neumann BCs 577—579
Programs, Laplace (Poisson) equation, five-point method, Dirichlet BCs 575—577
Programs, Laplace (Poisson) equation, Poisson equation 579—580
Programs, nonlinear equations, roots of 173—179
Programs, nonlinear equations, roots of, Newton’s method 173 174—176
Programs, nonlinear equations, roots of, secant method 173 176—177
Programs, nonlinear equations, roots of, systems of equations 173 177—179
Programs, numerical differentiation 273—278
Programs, numerical differentiation, direct fit polynomial 273—274
Programs, numerical differentiation, divided difference polynomial 276
Programs, numerical differentiation, Lagrange polynomial 275
Programs, numerical differentiation, Newton forward-difference polynomial 277—278
Programs, numerical integration 310—315
Programs, numerical integration, Romberg integration 313—315
Programs, numerical integration, Simpson’s 1/3 rule 312—313
Programs, numerical integration, trapezoid rule 310—312
Programs, parabolic PDEs 639—645
Programs, parabolic PDEs, BTCS method 642—643
Programs, parabolic PDEs, Crank — Nicolson method 643—645
Programs, parabolic PDEs, FTCS method 640—642
Programs, polynomial approximation 235—241
Programs, polynomial approximation, direct fit polynomial 235—236
Programs, polynomial approximation, divided difference polynomial 238
Programs, polynomial approximation, Lagrange polynomial 237
Programs, polynomial approximation, least squares polynomial 240—241
Programs, polynomial approximation, Newton forward-difference polynomial 239
Programs, systems of linear algebraic equations 67—75
Programs, systems of linear algebraic equations, Doolittle LU factorization 69—71
Programs, systems of linear algebraic equations, simple Gauss elimination 67—69
Programs, systems of linear algebraic equations, successive-over-relaxation (SOR) 73—75
Programs, systems of linear algebraic equations, Thomas algorithm 71—73
Projectile applied problems 431 432
Propagation path 510—511
Propagation path for the convection equation 506
Propagation path for the convection-diffusion equation 523
Propagation path for the Laplace equation 518
Propagation problems for hyperbolic PDEs see “Convection equation”
Propagation problems for parabolic PDEs see “Diffusion equation”
Propagation problems for PDEs, general concepts, asymptotic steady state solutions 637—639
Propagation problems for PDEs, general concepts, consistency 605—606
Propagation problems for PDEs, general concepts, convection, general features of 655—657
Propagation problems for PDEs, general concepts, convergence 605 610—611
Propagation problems for PDEs, general concepts, diffusion, general features of 592—593
Propagation problems for PDEs, general concepts, domain of dependence 592 655—656 657
Propagation problems for PDEs, general concepts, exact solutions for convection 652—653 656
Propagation problems for PDEs, general concepts, exact solutions for convection, diffusion 587—589
Propagation problems for PDEs, general concepts, explicit methods 594—595 599 657
Propagation problems for PDEs, general concepts, finite difference approximations 597—598 658—659
Propagation problems for PDEs, general concepts, finite difference approximations, space derivatives 598
Propagation problems for PDEs, general concepts, finite difference approximations, time derivatives 597—598
Propagation problems for PDEs, general concepts, finite difference equations 599
Propagation problems for PDEs, general concepts, finite difference grids 596 658
Propagation problems for PDEs, general concepts, fundamental considerations 591—596 657—658
Propagation problems for PDEs, general concepts, implicit methods 594—595 599 657
Propagation problems for PDEs, general concepts, implicit numerical diffusion 664—665
Propagation problems for PDEs, general concepts, implicit numerical dispersion 664—665
Propagation problems for PDEs, general concepts, information propagation speed, numerical 594 595
Propagation problems for PDEs, general concepts, information propagation speed, physical 592 595 655
Propagation problems for PDEs, general concepts, introduction to 587—591 651—655
Propagation problems for PDEs, general concepts, Lax equivalence theorem 610
Propagation problems for PDEs, general concepts, modified differential equation see “MDEs”
Propagation problems for PDEs, general concepts, order 605—606
Propagation problems for PDEs, general concepts, range of influence 592 655—656
Propagation problems for PDEs, general concepts, stability 606—610
Propagation problems for PDEs, general concepts, summary 645—646 701—702
Propagation problems for PDEs, stability analysis 606—610
| Propagation problems for PDEs, stability analysis, amplification factor 607
Propagation problems for PDEs, stability analysis, definition of 605
Propagation problems for PDEs, stability analysis, discrete perturbation method 607
Propagation problems for PDEs, stability analysis, examples 609—610 612 615 620 633 636 660 662 666—667 674 679 688—689
Propagation problems for PDEs, stability analysis, Fourier components 608
Propagation problems for PDEs, stability analysis, Fourier series 608
Propagation problems for PDEs, stability analysis, matrix method 607
Propagation problems for PDEs, stability analysis, methods of 607
Propagation problems for PDEs, stability analysis, nonlinear instability 607
Propagation problems for PDEs, stability analysis, von Neumann method 607—610
Propagation problems for PDEs, stability analysis, wave number 608
Propagation problems, ODEs 326
Propagation problems, PDEs 510 512—514
Pseudocode 3
QD method see “Quotient-Difference method”
QR factorization 105
QR method for eigenproblems 104—109
Quad precision 5
Quadratic convergence 149
Quadratic formula 156
Quadratic formula, rationalized 153 156
Quadrature see “Numerical integration”
Quadrature, definition of 285—286
Quadrature, introduction to 16
Quadrilateral elements, FEM 740—741
Quasilinear PDE, definition of 504
Quotient-Difference method 169
Rabinowitz, P. 111 169
Rachford, H.H. 618 627
Radiation heat transfer problem 336—338
Ralston, A. 111 169
Range of influence, convection equation 506 656
Range of influence, definition of 508
Range of influence, diffusion equation 520
Range of influence, Laplace equation 518
Range of influence, wave equation 523
Range of integration 291
Rao, S.S. 713
Rationalized quadratic formula 153 156
Rayleigh — Ritz approach to FEM 727—734
Rayleigh — Ritz approach to FEM, element equation 728
Rayleigh — Ritz approach to FEM, functional 727
Rayleigh — Ritz approach to FEM, nodal equation 728 731
Rayleigh — Ritz approach to FEM, numerical example 731—732 732—734
Rayleigh — Ritz method 438 714—719
Rayleigh — Ritz method for boundary-value problems 717—718
Rayleigh — Ritz method, basis of 716
Rayleigh — Ritz method, numerical example 718—719
Rayleigh — Ritz method, steps in 716
Reaction (chemical) rate applied problem 249—250
Real characteristics 511
Rectangular elements, FEM 740—741
Reddy, J.N 713
Redundant set of equations 19
Refining a root 129 133
Regula falsi method see “False position method”
Relative error 62
Relaxation (Southwell) method 64
Relaxation factor see “Over-relaxation factor”
Remainder term of Taylor polynomial 348
Remainder theorem for polynomials 194
Residual in linear system iterative methods 60 63 65
Residual methods for ODEs 719 721
Rice, J.R. 111
Richardson method, diffusion equation 611—612
Richardson method, parabolic PDEs 611
Richardson, L.F. 611
Richtmyer method see “Lax — Wendroff two-step method”
Richtmyer, R.D. 665 668
Rocket, vertical flight of 328—329 336—337 396 398—400
Romberg integration 297—299
Root finding see “Nonlinear equations roots
Roots of nonlinear equations see “Nonlinear equations roots
Roots of polynomials see “Polynomials roots
Roots, types of 133
Round-off effect on difference tables 210
Round-off error 5 52—54 351—352
Rounding, effects of 210
Row operations for linear systems 28 32
Row operations for linear systems, elimination 28
Row operations for linear systems, pivoting 28
Row operations for linear systems, scaling 28
Row vector 22
Runge — Kutta methods 370—378
Runge — Kutta methods, basic concept 370—371
Runge — Kutta methods, error control 376—378
Runge — Kutta methods, error estimation 376—378
Runge — Kutta methods, fourth-order method 372—376
Runge — Kutta methods, fourth-order method, program for 408—410
Runge — Kutta methods, Runge — Kutta — Fehlberg method 377—378
Runge — Kutta methods, Runge — Kutta — Merson method 421
Runge — Kutta methods, second-order method 371—372
Runge — Kutta methods, third-order method 420
Runge — Kutta — Fehlberg method 377—378
Runge — Kutta — Merson method 421
Scaled pivoting 37—39
Scaling 37
Schnabel, R.B. 173
Secant method see “Nonlinear equations roots
Secant to a curve 150
Shape functions for FEM 735 742—744 753
Shape functions for FEM, one-dimensional 726—727 735
Shape functions for FEM, two-dimensional 742—744
Sharp corner expansion applied problem 73
Shifted matrix 95
Shifted power method 95—101
Shifted power method for intermediate eigenvalues 97—99
Shifted power method for opposite extreme eigenvalue 95—97
Shifted power method to accelerate convergence 99—101
Shifting eigenvalues 95
Shooting method for boundary-value ODEs see “ODEs Boundary-value shooting
Significant digits 4
Similarity transformations 104
Simple elimination 35
Simple root 133—134
Simpson’s 1/3 rule 293—295
Simpson’s 3/8 rule 295—296
Simultaneous linear algebraic equations see “Systems of linear algebraic equations”
Single-point methods 364—378
Single-point methods, error estimation for 376—377
Single-point methods, fourth-order Runge — Kutta method 372—376
Single-point methods, implicit midpoint method 364—365
Single-point methods, implicit trapezoid method 368
Single-point methods, modified Euler method 368—370
Single-point methods, modified midpoint method 365—368
Single-point methods, modified trapezoid method 368
Single-point methods, Runge — Kutta methods 370—376
Single-point methods, second-order methods 364—370
Single-point methods, second-order Runge — Kutta method 371—372
Single-step methods for ODEs 364
Single-value methods for ODEs 364
Singular determinant 30
Singular matrix 30
Size of a matrix 22
Smith, B.T. et al. 111
Smoothly varying problems 350
Smoothness 350
Smoothness, nonsmoothly varying problems 350
Smoothness, smoothly varying problems 350
software packages 6—7
Software packages, Excel 6
Software packages, Macsyma 6
Software packages, Maple 6
Software packages, Mathcad 6
Software packages, Mathematica 6
Software packages, Matlab 7
Solutions Manual 4
SOR see “Systems of linear algebraic equations SOR”
Source terms 324 503
Southwell, R.V 64
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