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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 |
Interpolation, Newton backward-difference polynomial 213—215
Interpolation, Newton forward-difference polynomial 211—213
Interpolation, Stirling centered-difference polynomial 216
Interpolation, successive univariate polynomials 218—220
Interpolation, summary 242—243
Interval halving method 135—138
Interval, in numerical integration 291
Introduction Chapter 0 1—9
Introduction to basic tools of numerical analysis 11—16
Introduction to boundary-value ODEs 436—439
Introduction to eigenproblems 81—85
Introduction to elliptic PDEs 527—531
Introduction to hyperbolic PDEs 651—655
Introduction to initial-value ODEs 336—340
Introduction to interpolation 188—190
Introduction to nonlinear equations, roots of 127—130
Introduction to numerical differentiation 251—254
Introduction to numerical integration 285—288
Introduction to ODEs 323—333
Introduction to parabolic PDEs 587—591
Introduction to PDEs 501—502
Introduction to polynomial approximation 188—190
Introduction to systems of linear algebraic equations 18—21
Introduction to the book 1—10
Introduction to the finite element method 711—713
Inverse interpolation 217—218
Inverse of a matrix 26—27
Inverse of a matrix, evaluation by Doohttle LU factorization 48
Inverse of a matrix, evaluation by Gauss — Jordan elimination 42
Inverse power method for eigenvalues 92—95
Iteration error 5
Iteration for systems of linear algebraic equations 59—67
Iteration, BTCS approximation of the diffusion equation 626
Iteration, nonlinear boundary-value problems 471—474
Iterative improvement 58—59
Iterative methods 20
Iterative methods for eigenvalues see “Eigenproblems”
Iterative methods for systems of linear algebraic equations 59—67
Iterative methods for systems of linear algebraic equations, accuracy 62
Iterative methods for systems of linear algebraic equations, convergence 62—63
Iterative methods for systems of linear algebraic equations, Gauss — Seidel iteration 63—64
Iterative methods for systems of linear algebraic equations, Jacobi iteration 59—61
Iterative methods for systems of linear algebraic equations, over-relaxation factor 65—65
Iterative methods for systems of linear algebraic equations, successive-over-relaxation (SOR) 64—67
Iterative methods for the Laplace equation 543
Jacobi iteration 59—61
Jacobi method for eigenvalues 111
Jeeves, T.A. 152
Jenkins — Traub method 169
Jury problem 511
Lagged Newton’s method 149
Lagrange polynomials 198—204
Lagrange polynomials, differentiation of 255
Lagrange polynomials, fitting 199
Lagrange polynomials, interpolation with 200—201
Lagrange polynomials, Neville’s algorithm 201—204
Lagrange polynomials, program for 237
Laguerre’s method 169
Languages see “Programming languages”
LAPACK 7
Laplace equation 502 512 516 526 528 530 Chapter
Laplace equation, boundary conditions 531
Laplace equation, coefficient matrix size 543
Laplace equation, compact fourth-order method 557—561
Laplace equation, consistency 544—545
Laplace equation, control volume method 571—575
Laplace equation, convergence 545—546
Laplace equation, convergence criteria 547
Laplace equation, derivative BCs 550—553
Laplace equation, direct methods 537—541
Laplace equation, exact problem 528—530
Laplace equation, example problem 528—530
Laplace equation, extrapolation 561—562
Laplace equation, finite difference approximations 534—535
Laplace equation, finite difference grids 533—534
Laplace equation, finite element method (FEM) 712—713 740—752
Laplace equation, five-point method 536—537
Laplace equation, Gauss — Seidel method 546—548
Laplace equation, grid aspect ratio 536
Laplace equation, higher-order methods 557—562
Laplace equation, initial guess, effect of 549—550
Laplace equation, introduction to 527—531
Laplace equation, iterative methods 546—550
Laplace equation, nonhomogeneous see “Poisson equation”
Laplace equation, nonrectangular domain 562—570
Laplace equation, numerical examples 540—542 547—548 549—550 552—553 559—561 561—562 565—568 574—575
Laplace equation, numerical methods, compact fourth-order method 557—561
Laplace equation, numerical methods, control volume method 571—575
Laplace equation, numerical methods, finite element method 740—752
Laplace equation, numerical methods, five-point method 536—537
Laplace equation, numerical methods, Gauss — Seidel method 546—548
Laplace equation, numerical methods, iterative methods 546—550
Laplace equation, numerical methods, SOR method 548—550
Laplace equation, numerical methods, successive-over-relaxation method 548—550
Laplace equation, operation count 542—543
Laplace equation, order 537
Laplace equation, over-relaxation factor 548—549
Laplace equation, over-relaxation factor, optimum 549
Laplace equation, packages 580
Laplace equation, programs for 575—580
Laplace equation, residual 546 548
Laplace equation, solution domain 532—534
Laplace equation, SOR method 548—550
Laplace equation, successive-over-relaxation (SOR) method 548—550
Laplace equation, summary 580—581
Laplace equation, system equation 540
Laplace equation, three-dimensional problems 571
Laplacian operator 503
Lax equivalence theorem 610 615 620 634 636 662
Lax method 659—664
Lax method, amplification factor 660
Lax method, finite difference equation 659
Lax method, modified differential equation 662
Lax method, numerical solution using 663
Lax method, stability analysis 662
Lax — Wendroff (Richtmyer) two-step method 668—670
Lax — Wendroff (Richtmyer) two-step method, finite difference equations 668
Lax — Wendroff (Richtmyer) two-step method, finite difference stencil 669
Lax — Wendroff (Richtmyer) two-step method, numerical example 669—670
Lax — Wendroff one-step method 665—668
Lax — Wendroff one-step method, convection equation 665—668
Lax — Wendroff one-step method, convection equation, amplification factor G 666
Lax — Wendroff one-step method, convection equation, finite difference equation 666
Lax — Wendroff one-step method, convection equation, finite difference stencil 666
Lax — Wendroff one-step method, convection equation, modified differential equation 666
Lax — Wendroff one-step method, convection equation, numerical example 667—668
Lax — Wendroff one-step method, convection equation, stability analysis 666—667
Lax — Wendroff one-step method, wave equation 687—690
Lax — Wendroff one-step method, wave equation, amplification matrix G 688
Lax — Wendroff one-step method, wave equation, finite difference equations 688
Lax — Wendroff one-step method, wave equation, modified differential equation 688
Lax — Wendroff one-step method, wave equation, numerical example 689—690
Lax — Wendroff one-step method, wave equation, stability analysis 688—689
Lax — Wendroff type methods 665—673
Lax — Wendroff type methods, Lax — Wendroff (Richtmyer) two-step method 668—670
Lax — Wendroff type methods, Lax — Wendroff one-step method 665—668
Lax — Wendroff type methods, MacCormack method 670—673
Lax, P.D. 610 661 665 668 687
Leapfrog method 611—613
Least squares approximation 225—234
Least squares approximation, deviations 225
Least squares approximation, examples 227—228 230—231 232—233
Least squares approximation, higher-degree polynomials 228—231
Least squares approximation, introduction to 225—227
Least squares approximation, multivariate polynomials 231—233
Least squares approximation, nonlinear functions 234
Least squares approximation, normal equations 227
Least squares approximation, program for 240—241
Least squares approximation, straight line 227—228
Lehmer — Schur method 169
| Lewy, H. 662
Libraries, software 6—7
Libraries, software, GAMS 7
Libraries, software, IMSL 7
Libraries, software, LAPACK 7
Libraries, software, NAG 7
Libraries, software, NETLIB 7
Linear differential equations, first-order initial-value ODE 340—341
Linear differential equations, ordinary differential equations 324
Linear differential equations, partial differential equations 503
Linear differential equations, second-order boundary-value ODE 439—440
Linear element in FEM 727
Linear equations see “Systems of linear algebraic equations”
Linear systems see “Systems of linear algebraic equations”
Linearization of nonlinear ODEs 342 361—362
Linearization of nonlinear PDEs 626—627
LINPACK 75
Lower triangular matrix 23
LU factorization 27 45—48
LU factorization, Crout method 45
LU factorization, Doolittle method 46—48
MacCormack method 670—673
MacCormack method, finite difference equations 671
MacCormack method, finite difference stencil 672
MacCormack method, numerical example 672
MacCormack, R.W 665 670
Machine accuracy 62
Machine vibration applied problem 431
Maclaurin series 8
Macsyma 6 75 179 241 488
Major diagonal of a matrix 23
Maple 6 75 179 242 413 488
Mastin, C.W. 570
Mathcad 6 131 179 241 413 488
Mathematica 6 75 179 241 413 488
MATLAB 7 131 179 241 413 488
Matrices 21—28
Matrices, addition 24
Matrices, associative property of 24
Matrices, augmented matrix 35—36
Matrices, banded matrix 24
Matrices, block tridiagonal matrix 52
Matrices, commutative property of 25
Matrices, conformable matrices 25
Matrices, definition of 22—24
Matrices, deflation 111
Matrices, determinant of 28—30
Matrices, determinants see “Determinants”
Matrices, diagonal matrix 23
Matrices, diagonally dominant 24
Matrices, distributive property of 26
Matrices, division 24
Matrices, elementary algebra 24—27
Matrices, elementary properties of 21—27
Matrices, factorization 27
Matrices, identity matrix 23
Matrices, ill conditioned matrix 54—55
Matrices, inverse matrix 26—27
Matrices, inverse matrix by Doolittle LU method 48
Matrices, inverse matrix by Gauss — Jordan elimination 42
Matrices, lower triangular matrix 23
Matrices, LU factorization 27 45—48
Matrices, major diagonal 23
Matrices, multiplication 24
Matrices, nonsingular 30
Matrices, notation 22
Matrices, numerical examples 25—26
Matrices, partitioned 27
Matrices, QR factorization 104—107
Matrices, row operations 28
Matrices, singular 30
Matrices, size 22
Matrices, sparse matrix 24
Matrices, square matrix 23
Matrices, subtraction 24
Matrices, symmetric matrix 24
Matrices, systems of linear algebraic equations 27—28
Matrices, transpose matrix 24
Matrices, triangular matrix 23
Matrices, tridiagonal matrix 24 49—52
Matrices, unity matrix 23
Matrices, upper triangular matrix 23
Matrix deflation 111
Matrix method of stability analysis 607
Matrix notation 22
Matrix partitioning 27
McDonald, A.T. 521
MDE, acronym 544 605
MDEs for ODEs 360—361
MDEs for PDEs 544
MDEs, convection equation 660 662 666 673 676 679
MDEs, convection-diffusion equation 633 636
MDEs, definition of 360 544
MDEs, diffusion equation 606 613 615 620 625
MDEs, Laplace equation 544—545
MDEs, wave equation 688
Merson method see “Runge — Kutta — Merson method”
Midpoint method 364—365
Minimax criterion 226
Mixed boundary conditions, boundary-value ODEs 441 464
Mixed boundary conditions, boundary-value ODEs, equilibrium method 464
Mixed boundary conditions, boundary-value ODEs, shooting method 464
Mixed boundary conditions, PDEs 523
Mixed elliptic/hyperbolic problems 637—639
Mixed elliptic/parabolic problems 637—639
Mode of oscillation 83 88
Model equations, ODE stability analysis 362
Model equations, PDEs 524—525
Model equations, stiff ODE 402—403
Modified differential equation see “MDE”
Modified Euler method 368—370
Modified Euler method, consistency 368
Modified Euler method, example 369—370
Modified Euler method, order 369
Modified Euler method, stability 369
Modified midpoint method 365—368
Modified midpoint method, consistency 365—366
Modified midpoint method, example 366—368
Modified midpoint method, order 366
Modified midpoint method, stability 366
Momentum equation see “Newton’s second law of motion”
Mop up 391
Muller, D.E. 152 169
Muller’s method 141 152—155
Muller’s method, convergence rate of 155
Multidimensional approximation see “Multivariate approximation”
Multidimensional interpolation see “Multivariate interpolation”
Multidimensional problems, elliptic PDEs 571
Multidimensional problems, hyperbolic PDEs 682—683
Multidimensional problems, parabolic PDEs 627—629
Multigrid method 571 580
Multiple b vectors 36
Multiple integrals 306—310
Multiple root 133—134
Multipoint methods for ODEs 381—391
Multipoint methods for ODEs, Adams FDEs 383
Multipoint methods for ODEs, Adams — Bashforth FDEs 383
Multipoint methods for ODEs, Adams — Bashforth — Moulton FDEs 383
Multipoint methods for ODEs, Adams — Moulton FDEs 383
Multipoint methods for ODEs, concept 381—383
Multipoint methods for ODEs, explicit Adams — Bashforth FDEs 388—389
Multipoint methods for ODEs, explicit multipoint methods 382
Multipoint methods for ODEs, fourth-order Adams — Bashforth method 383—384
Multipoint methods for ODEs, fourth-order Adams — Bashforth — Moulton method 386 387—388
Multipoint methods for ODEs, fourth-order Adams — Moulton method 385
Multipoint methods for ODEs, general Adams methods 388—390
Multipoint methods for ODEs, implicit Adams — Moulton FDEs 389—390
Multipoint methods for ODEs, implicit multipoint methods 382—383
Multistep methods for ODEs 382
Multivalue methods for ODEs 382
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