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Hoffman J.D. Numerical Methods for Engineers and Scientists
Hoffman J.D.  Numerical Methods for Engineers and Scientists









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: Numerical Methods for Engineers and Scientists

: Hoffman J.D.

:

Hoffman (mechanical engineering, Purdue U.) introduces engineers and scientists to numerical methods that can be used to solve mathematical problems arising in engineering and science that cannot be solved by exact methods. His general approach is to introduce a type of problem, present sufficient background to understand the problem and possible methods of solving it, develop one or more numerical methods, and illustrate the methods with examples. He include bad methods as well as good to clarify why some work and some do not. He has significantly revised the first edition, published by McGraw-Hill in 1992, and added a new section with several FORTRAN programs for implementing the algorithms developed.Copyright 2004 Book News, Inc., Portland, OR


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ed2k: ed2k stats

: second edition

: 2001

: 823

: 23.02.2005

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Abramowitz, M.      290 296 303
Absolute error      62
Accelerating convergence of eigenprobleras      99101
Accuracy      4 62
Accuracy, criterion      62
Accuracy, machine      62
Acoustic wave propagation      514 521523 684686
Acoustic wave propagation, exact solution      685686
Acoustics      521
Acoustics, example problem      652654
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      383384
Adams Bashforth fourth-order FDE, stability analysis      386387
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      383388
Adams Bashforth Moulton fourth-order method, example      387
Adams Bashforth Moulton fourth-order method, program for      412413
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      299302
ADI method      see Alternating-direction implicit method
Adjusted system equation (FEM)      725
AFI method      see Approximate-factorization implicit method
Aitkens 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      627628
Amplification factor G for ODEs, definition of      361
Amplification factor G for ODEs, for FDEs      361 363 366 369 374 386387
Amplification factor G for PDEs, convection equation FDEs      660 662 666 674 676 679
Amplification factor G for PDEs, convection-diffusion equation FDEs      633636
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      688689
Application subroutine      3
Applied problems, definition of      4
Approach of the book      1
Approximate fits      189190 225
Approximate Newtons 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      623629
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      756758
Assembling finite element equations, Laplace (Poisson) equation      748750
Associative property of matrices      24
Asymptotic steady-state solution of PDEs      637639
Auxiliary conditions, ODEs      324 325
Auxiliary conditions, PDEs      524525
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
Bairstows method      164167
Banded matrix      24
Banded matrix for the five-point method      539
Bashforth, E      383
BASIC      3
Basic Tools of Numerical Analysis, Part I      1116
BC, acronym      441
BCs      see Boundary conditions
Beam (laterally loaded)      331 436437
Beam applied problems      498499
Bessel centered-difference polynomial      216
Best manner possible fit      189190 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      524525
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 130133
Bracketing methods      129 133 135140
Brandt, A.      571 580
Brent, R.P.      169
Brents method      169
BTCS method, convection equation      677682
BTCS method, convection-diffusion equation      635637
BTCS method, diffusion equation      614619
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      260261 267268 271
CFL stability criterion      see Courant Friedrichs Lewy stability criterion
Chapra, S.C.      222
Characteristic concepts for hyperbolic PDEs      656657
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      509510
Characteristic paths for first-order PDEs      506 509
Characteristic paths for hyperbolic PDEs      514515
Characteristic paths for parabolic PDEs      513514
Characteristic paths for PDEs      505515
Characteristic paths for second-order PDEs      507508
Characteristic paths for the convection equation      506 507 509
Characteristic paths for the convection-diffusion equation      523524
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      505506 526
Chemical reaction applied problem      432433
Circular pyramid volume applied problem      321
Classification of ODEs      325326
Classification of PDEs      504511
Classification of physical problems      326327 511516
Closed domain      327 511
Closed domain methods      see Nonlinear equations roots
Colebrook equation applied problem      186
Colebrook, C.F.      186
Collocation method      438 719721
Collocation method for boundary-value problem      720
Collocation method, numerical example      720721
Collocation method, steps in      719720
Column vector      22
Commutative property of matrices      25
Compact fourth-order approximations, first derivative      468
Compact fourth-order approximations, second derivative      468469
Compact fourth-order method, boundary-value ODEs      467471
Compact fourth-order method, PDEs      557561
Compatibility equation      507
Complementary solution of ODEs      340341 440
Complex characteristics      511
Complex roots of polynomials      158 162163
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      359361 365366 368369 373 378 384 385
Consistency for PDE methods, elliptic PDEs      544545
Consistency for PDE methods, hyperbolic PDEs      660 662 666 674 676 679 688
Consistency for PDE methods, parabolic PDEs      605606 613 615 620 633
Continuity equation      520
Control volume discretization      571574
Control volume method      571575
Convection      506
Convection equation      506 521 526 652653 655656
Convection equation, characteristic equation for      506
Convection equation, compatibility equation for      506
Convection equation, exact solution of      652653 656
Convection equation, Numerical examples      661 662664 667668 669670 672 674675 676677 680682
Convection equation, numerical methods, BTCS method      677682
Convection equation, numerical methods, FTCS method      659661
Convection equation, numerical methods, Lax method      661664
Convection equation, numerical methods, Lax Wendroff one-step method      665668
Convection equation, numerical methods, Lax Wendroff two-step method      668670
Convection equation, numerical methods, MacCormack method      670673
Convection equation, numerical methods, upwind methods      673677
Convection equation, programs for      691701
Convection number, definition of      633 660
Convection of heat      330
Convection, definition of      506
Convection, general features of      506 655656
Convection-diffusion equation      523524 526 629637
Convection-diffusion equation, asymptotic steady-state solution      638639
Convection-diffusion equation, BTCS method      635637
Convection-diffusion equation, exact solution of      630632
Convection-diffusion equation, FTCS method      633635
Convection-diffusion equation, introduction to      629632
Convection-diffusion equation, numerical examples      634635 636637 638639
Convection-diffusion equation, numerical methods, asymptotic steady-state solution      637639
Convection-diffusion equation, numerical methods, BTCS method      635637
Convection-diffusion equation, numerical methods, FTCS method      633635
Convergence criteria      547
Convergence rate, fixed-point iteration      144145
Convergence rate, Newtons method for roots      147149
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      610611
Converging solutions of ODEs      351
Courant Friedrichs Lewy stability criterion      662
Courant, R.      662
Cramers Rule      3132
Cramers rule in characteristic analysis      507
Cramers rule in eigenproblems      8586
Crank Nicolson method      619623
Crank Nicolson method, diffusion equation      619623
Crank Nicolson method, system equation for      620
Crank, J.      619
Crout LU factorization method      45
Cubic splines      221225
Curve fitting      see Polynomial approximation
Cylindrical coordinates      563
Deflated polynomial      195
Deflation of matrices      111
Deflation of polynomials      159160 195196
Deflation technique for eigenvalues      111
Dennis, J.E.      173
Derivative BCs, boundary-value ODEs      458464
Derivative BCs, elliptic PDEs      550552
Derivative BCs, finite element method      735 745 754
Derivative BCs, parabolic PDEs      623625
Derivative function for ODEs      324 338
Descartes Rule of Signs      156
Determinants      2830
Determinants, cofactor of      29
Determinants, definition of      28
Determinants, evaluation by cofactors      29
Determinants, evaluation by diagonal method      2830
Determinants, evaluation by elimination      4345
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      262264
Difference formulas from Taylor series      270271
Difference formulas, introduction to      15
Difference formulas, table of      271
Difference polynomials      208 211216
Difference polynomials, Bessel centered-difference      216
Difference polynomials, Newton backward-difference      213215
Difference polynomials, Newton forward-difference      211213
Difference polynomials, Stirling centered-difference      216
Difference tables      208211
Difference tables, backward      209
Difference tables, centered      209
Difference tables, definition of      208209
Difference tables, example of      209
Difference tables, forward      209
Difference tables, polynomial fitting      210211
Difference tables, round-off errors      210
Differences      208211
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 194195
Differentiation, Numerical      see Numerical differentiation
Diffusion equation      502 512513 519520 526 587589
Diffusion equation, classification of      519520
Diffusion equation, derivative BCs      623626
Diffusion equation, domain of dependence      520 594
Diffusion equation, exact solution of      588589 592593
Diffusion equation, example problem      587589
Diffusion equation, finite element solution of      712713
Diffusion equation, general features of      592593
Diffusion equation, implicit methods      613623
Diffusion equation, introduction to      592593
Diffusion equation, multidimensional problems      627629
Diffusion equation, nonlinear equations      625626
Diffusion equation, numerical examples      600605 616618 621623 625626 758759
Diffusion equation, numerical methods, BTCS method      614619
Diffusion equation, numerical methods, Crank Nicolson method      619623
Diffusion equation, numerical methods, derivative BCs      623625
Diffusion equation, numerical methods, DuFort Frankel method      613
Diffusion equation, numerical methods, finite element method      752759
Diffusion equation, numerical methods, FTCS method      599605
Diffusion equation, numerical methods, Richardson method      611613
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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