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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 |
ODEs, boundary value, shooting method, mixed boundary condition 464
ODEs, boundary value, shooting method, nonlinear boundary-value problem 471
ODEs, boundary value, shooting method, numerical examples 444—447 447—448 448—449 460—461
ODEs, boundary value, shooting method, order 442
ODEs, boundary value, shooting method, second-order boundary-value ODE 442—449
ODEs, boundary value, shooting method, second-order shooting method 444—448
ODEs, boundary value, shooting method, stability 442
ODEs, boundary value, shooting method, summary 488—490
ODEs, boundary value, shooting method, superposition of solutions 447—448
ODEs, boundary value, summary 441 488—490
ODEs, boundary value, systems of ODEs 441
ODEs, boundary-value ODEs 325 330—332
ODEs, boundary-value, shooting method, numerical methods, extrapolation 448—449
ODEs, boundary-value, shooting method, numerical methods, implicit trapezoid method 444—447
ODEs, boundary-value, shooting method, numerical methods, modified Euler method 444
ODEs, boundary-value, shooting method, numerical methods, Runge — Kutta method 446—447
ODEs, classification of ODEs 325—326
ODEs, classification of ODEs, boundary-value 325
ODEs, classification of ODEs, initial-value 326
ODEs, closed domain 326
ODEs, constant coefficient 324
ODEs, derivative function 324
ODEs, eigenproblems 327
ODEs, equilibrium problems 327
ODEs, examples, heat conduction 330—331
ODEs, examples, heat radiation 328—329
ODEs, examples, laterally loaded beam 331—332
ODEs, examples, rocket flight 329—330
ODEs, families of solutions 325
ODEs, forcing function 324
ODEs, general features of 323—325
ODEs, general first-order ODE 325 333
ODEs, general second-order ODE 325 333
ODEs, homogeneity 324—325
ODEs, initial value, numerical methods, Adams methods 383
ODEs, initial value, numerical methods, Adams — Bashforth method 383—385 388—389
ODEs, initial value, numerical methods, Adams — Bashforth — Moulton method 387—388
ODEs, initial value, numerical methods, Adams — Moulton method 385—386 389—390
ODEs, initial value, numerical methods, Bulirsch — Stoer method 381
ODEs, initial value, numerical methods, explicit Euler method 352—355
ODEs, initial value, numerical methods, explicit Euler method, comparison to implicit Euler method 357—359
ODEs, initial value, numerical methods, extrapolated modified midpoint method 378—381
ODEs, initial value, numerical methods, extrapolation methods 378—381
ODEs, initial value, numerical methods, Gear’s methods 407—408
ODEs, initial value, numerical methods, Heun method 368
ODEs, initial value, numerical methods, implicit Euler method 355—357
ODEs, initial value, numerical methods, implicit Euler method, comparison to explicit Euler method 357—359
ODEs, initial value, numerical methods, implicit midpoint method 365
ODEs, initial value, numerical methods, implicit trapezoid method 368
ODEs, initial value, numerical methods, modified Euler method 368—370
ODEs, initial value, numerical methods, modified midpoint method 365—368
ODEs, initial value, numerical methods, modified trapezoid method 368
ODEs, initial value, numerical methods, multipoint methods 381—391
ODEs, initial value, numerical methods, predictor-corrector methods 249—251 383—388
ODEs, initial value, numerical methods, Runge — Kutta methods 370—376
ODEs, initial value, numerical methods, single-point methods 364—378
ODEs, initial value, numerical methods, summary 414—416
ODEs, initial value, numerical methods, systems of ODEs 397—400
ODEs, initial value, numerical methods, Taylor series method 343—346
ODEs, initial-value Chapter 7 335—433
ODEs, initial-value ODEs 325 327—330
ODEs, initial-value, consistency 349 359—361 364
ODEs, initial-value, convergence 360 363 364
ODEs, initial-value, definition of 323 327—330
ODEs, initial-value, derivative function 338
ODEs, initial-value, equivalence theorem for convergence 363
ODEs, initial-value, error control 390—391
ODEs, initial-value, error estimation 390—391
ODEs, initial-value, errors 351—352
ODEs, initial-value, exact solution of 340 341
ODEs, initial-value, example problems 327—330 336—338 398
ODEs, initial-value, extrapolation 390—391
ODEs, initial-value, extrapolation methods 378—381
ODEs, initial-value, families of solutions 341—342
ODEs, initial-value, finite difference approximations 347—349
ODEs, initial-value, finite difference equations 349—350
ODEs, initial-value, finite difference girds 346—347
ODEs, initial-value, finite difference method 346—352
ODEs, initial-value, general features of 340—343
ODEs, initial-value, general nonlinear first-order ODE 338
ODEs, initial-value, higher-order ODEs 342—343 396—397
ODEs, initial-value, higher-order ODEs, single-point methods 364—378
ODEs, initial-value, introduction to 327—330 336—340
ODEs, initial-value, linear first-order ODE 340—341
ODEs, initial-value, multipoint methods 381—391
ODEs, initial-value, multistep methods 382
ODEs, initial-value, multivalue methods 382
ODEs, initial-value, nonlinear first-order ODE 341—342
ODEs, initial-value, nonlinear implicit FDEs 383—396
ODEs, initial-value, nonlinear implicit FDEs, Newton’s method 394—396
ODEs, initial-value, nonlinear implicit FDEs, time linearization 393—394
ODEs, Initial-value, numerical examples 344—346 354—355 356—357 366—368 369—370 374—376 379—381 387—388 393—394 395 398—400 403 404—405
ODEs, initial-value, order 359—361 364
ODEs, initial-value, packages 413
ODEs, initial-value, programs for 408—413
ODEs, initial-value, single-point methods 364—378
ODEs, initial-value, single-step methods 364
ODEs, initial-value, single-value methods 364
ODEs, initial-value, smoothness 350
ODEs, initial-value, stability 360 361—363 364
ODEs, initial-value, stiff ODEs 400—408
ODEs, initial-value, summary 343 414—416
ODEs, initial-value, summary of methods 391—393
ODEs, initial-value, summary of results 391—393
ODEs, initial-value, systems of 343 397—400
ODEs, introduction to 323 330—332
ODEs, linear 324
ODEs, nonlinear 324
ODEs, open domain 325
ODEs, order of 324
ODEs, physical problem classification 326—327
ODEs, physical problem classification, eigenproblems 327
ODEs, physical problem classification, equilibrium 326—327
ODEs, physical problem classification, propagation 326—327
ODEs, propagation problems 327
ODEs, source term 324
ODEs, summary 332—333
ODEs, systems of ODEs 325
ODEs, time-like coordinate 327
ODEs, time-like direction 327
ODEs, variable coefficient 324
One-dimensional boundary-value problems see “ODEs boundary
One-dimensional initial-value problems see “ODEs initial
One-sided difference formulas 268
Open domain for ODEs 326
Open domain for PDEs 512 513
Open domain methods see “Nonlinear equations roots
Opposite extreme eigenvalue 95—97
Optimum over-relaxation factor 65—67
Optimum over-relaxation factor for five-point method 549—550
Optimum over-relaxation factor, effect of grid aspect ratio on 549
Order of difference formulas 267
Order of FDAs of boundary-value ODEs 442 450
Order of FDAs of elliptic PDEs 535 545
Order of FDAs of initial-value ODEs 359—361
Order of FDAs of parabolic PDEs 605—606
Order of ODEs 324
Order of PDEs 503
Ordinary differential equations see “ODEs”
Organization of the book 2
Over-relaxation see “Successive-over-relaxation”
Over-relaxation factor 65—67
Over-relaxation factor for the five-point method 548—550
Over-relaxation factor, optimum value of 65—67 549
Overshoot 358
Packages, boundary-value ODEs 488
Packages, eigenproblems 118
Packages, elliptic PDEs 580
Packages, finite element method 769
Packages, hyperbolic PDEs 701
| Packages, initial-value ODEs 413
Packages, nonlinear equation, roots of 179
Packages, numerical differentiation 278—279
Packages, numerical integration 315
Packages, parabolic PDEs 645
Packages, polynomial approximation 241—242
Packages, systems of linear algebraic equations 118
Parabolic PDEs Chapter 10 587—650
Parabolic PDEs, asymptotic steady-state solutions 637—639
Parabolic PDEs, backward-time centered-space (BTCS) method 614—619
Parabolic PDEs, consistency 605—606
Parabolic PDEs, convection-diffusion equation 522 629—637
Parabolic PDEs, convergence 610—111
Parabolic PDEs, Crank — Nicolson method 619—623
Parabolic PDEs, definition of 505
Parabolic PDEs, diffusion equation 519
Parabolic PDEs, forward-time centered-space (FTCS) method 599—605
Parabolic PDEs, general features of 512—515 591—593
Parabolic PDEs, introduction to 587—591
Parabolic PDEs, order 605—606
Parabolic PDEs, packages 645
Parabolic PDEs, programs for 639—645
Parabolic PDEs, stability 605—610
Parabolic PDEs, summary 645—646
Parabolic PDEs, the finite difference method for 593—599
Part I, basic tools of numerical analysis 11—16
Part II, ordinary differential equations 323—333
Part III, partial differential equations 501—526
Partial differential equations see “PDEs”
Partial pivoting 36
Particular solution of ODEs 340—341 440
Pascal 3
Path of propagation see “Propagation path”
Pathline 506 656
Pathline for the convection equation 506
Pathline for the convection-diffusion equation 522
PDE, acronym 501
PDEs Part III 501—526:
PDEs, auxiliary conditions 524—525
PDEs, boundary conditions 524
PDEs, Cauchy problem 525
PDEs, characteristic curves (paths) 505—506 509 510 513 514 520 522 526
PDEs, characteristic equation 506 507 520 522
PDEs, classification of PDEs 504—511
PDEs, classification of physical problems 511—516
PDEs, closed domain 511
PDEs, compatibility equation 507
PDEs, complex characteristics 510
PDEs, conic sections 505
PDEs, convection equation see “Convection equation”
PDEs, convection-diffusion equation see “Convection-diffusion equation”
PDEs, definition of PDE 502
PDEs, diffusion equation see “Diffusion equation”
PDEs, Dirichlet BC 524
PDEs, discontinuous derivatives 506—507
PDEs, discriminant of PDEs 505 510 517 519 522 523
PDEs, domain of dependence 508
PDEs, domain of dependence, elliptic PDEs 508 512 518 531
PDEs, domain of dependence, hyperbolic PDEs 508 523 655 657
PDEs, domain of dependence, parabolic PDEs 508 520 592 593
PDEs, eigenproblems 515—516
PDEs, elliptic PDEs 505 516—519
PDEs, equilibrium problems 511
PDEs, examples of convection equation see Chapter 11
PDEs, examples of convection-diffusion equation see Chapter 10
PDEs, examples of diffusion equation see Chapter 10
PDEs, examples of Laplace (Poisson) equation see Chapter 9
PDEs, examples of wave equation see Chapter 11
PDEs, examples, acoustic wave propagation 514—515 520—523
PDEs, examples, convection 506 521
PDEs, examples, steady heat diffusion 512 516—517
PDEs, examples, unsteady heat diffusion 513 519
PDEs, general features of 502—504
PDEs, general features, table of 516
PDEs, general quasilinear first-order PDE 504 508—509
PDEs, general quasilinear second-order PDE 504 507—508
PDEs, general system of quasilinear first-order PDEs 504 509—510
PDEs, homogeneity 503
PDEs, hyperbolic PDEs 505 511 520—523
PDEs, information propagation path 510 518 520 523
PDEs, information propagation speed 510 520 523
PDEs, initial values 524—525
PDEs, initial-value problem 512
PDEs, introduction to 501—502
PDEs, jury problem 511
PDEs, Laplace equation see “Laplace (Poisson) equation”
PDEs, linear PDE 503
PDEs, mixed BC 524
PDEs, Neumann BC 524
PDEs, nonhomogeneous term 50
PDEs, nonlinear PDE 503
PDEs, open domain 512
PDEs, order of a PDE 503
PDEs, parabolic PDEs 505 511 519—520
PDEs, path of propagation 506 510—511
PDEs, pathline 506
PDEs, physical problem classification 511—516
PDEs, Poisson equation see “Laplace (Poisson) equation”
PDEs, propagation problems 511 512—515
PDEs, range of influence 508
PDEs, range of influence, elliptic PDEs 509 510—511
PDEs, range of influence, hyperbolic PDEs 510 523
PDEs, range of influence, parabolic PDEs 510 520
PDEs, space-like coordinate 513
PDEs, substantial derivative 521
PDEs, summary 526
PDEs, systems of PDEs 504
PDEs, time-like coordinate 513
PDEs, types of PDEs 504—511
PDEs, variable coefficient 503
PDEs, wave equation see “Wave equation”
PDEs, well posed problems 525
Peaceman, D.W 618 627
Peclet number 632
Pendulum applied problems 432
Physical information propagation speed 454 455
Physical problems governed by ODEs, classification of 326—327
Physical problems governed by ODEs, eigenproblems 326—327
Physical problems governed by ODEs, equilibrium problems 326—327
Physical problems governed by ODEs, propagation problems 326—327
Physical problems governed by PDEs 511—515
Physical problems governed by PDEs, classification of 511—515
Physical problems governed by PDEs, eigenproblems 514—515
Physical problems governed by PDEs, equilibrium problems 512
Physical problems governed by PDEs, propagation problems 512—514
Piecewise approximation for interpolation 221
Pitfalls of elimination methods 52—59
Pitfalls of root finding methods 150 167—169
Pivoting 36—37
Poisson equation 503 518 530 552—556
Poisson equation, five-point method for 554—555
Poisson equation, numerical example 555—556
Polishing roots 149 157
Polynomial approximation Chapter 4 187—250
Polynomial approximation, approximate fits 189
Polynomial approximation, approximating functions 188—190
Polynomial approximation, Bessel polynomial 216
Polynomial approximation, cubic splines 221—225
Polynomial approximation, difference polynomials 211—216
Polynomial approximation, difference tables 208—210
Polynomial approximation, differentiation 251—284
Polynomial approximation, direct fit multivariate polynomials 218—220
Polynomial approximation, direct fit polynomials 197—198
Polynomial approximation, divided difference polynomials 204 206—208
Polynomial approximation, divided difference tables 204—206
Polynomial approximation, exact fits 189
Polynomial approximation, general features of 188—190
Polynomial approximation, integration 285—321
Polynomial approximation, interpolation 187—250
Polynomial approximation, introduction to 14 188—199
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