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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 |
Multivariate interpolation 218—220
Multivariate interpolation, direct multivariate polynomial 220
Multivariate interpolation, least squares polynomials 231—233
Multivariate interpolation, successive univariate polynomials 218—220
Multivariate polynomials 218—220
Multivariate polynomials, direct multivariate polynomials 220
Multivariate polynomials, least squares polynomials 231—233
Multivariate polynomials, successive univariate polynomials 218—220
NAG 7
Nested multiplication algorithm 194 195—196
NETLIB 7
Neumann boundary conditions for boundary-value ODEs 441
Neumann boundary conditions for PDEs 524
Neville’s algorithm 201—204
Newton backward-difference polynomial 213—215
Newton backward-difference polynomial, differentiation of 261—262
Newton backward-difference polynomial, error of 215
Newton backward-difference polynomial, example 214—215
Newton backward-difference polynomial, fitting 213—214
Newton backward-difference polynomial, interpolation with 214—215
Newton forward-difference polynomial 257—261
Newton forward-difference polynomial, differentiation of 257—261
Newton forward-difference polynomial, error of 213
Newton forward-difference polynomial, example 212—213
Newton forward-difference polynomial, fitting 211—212
Newton forward-difference polynomial, integration of 290—291
Newton forward-difference polynomial, interpolation with 212—213
Newton forward-difference polynomial, program for 239
Newton — Cotes formulas 290—297
Newton — Cotes formulas, coefficients, table of 297
Newton — Cotes formulas, definition of 290
Newton — Cotes formulas, derivation of 290—297
Newton — Raphson method see “Nonlinear equations roots Newton’s
Newton’s Law of Cooling 330
Newton’s method for nonlinear implicit FDEs 394—396
Newton’s method for nonlinear, boundary-value problems 474—477
Newton’s method for roots of nonlinear equations see “Nonlinear equations roots Newton’s
Newton’s method for systems of nonlinear equations 170—173 444
Newton’s second law of motion in eigenproblems 81
Newton’s second law of motion, dynamic spring-mass system 81
Newton’s second law of motion, flight of a rocket 329
Newton’s second law of motion, fluid mechanics 520
Nicolson, P. 619
Nodal equations, FEM, boundary-value ODE 736 738
Nodal equations, FEM, diffusion equation 758
Nodal equations, FEM, Laplace (Poisson) equation 750
Nonbracketing methods 129 133 140—155
Nonconformable matrices 25
Nonhomogeneous, ordinary differential equations 325
Nonhomogeneous, partial differential equation 503
Nonhomogeneous, partial differential equation, elliptic 570—571
Nonhomogeneous, partial differential equation, hyperbolic 682
Nonhomogeneous, partial differential equation, parabolic 625—627
Nonhomogeneous, partial differential equations 504
Nonhomogeneous, system of linear algebraic equations 19
Nonlinear boundary-value problems 471—477
Nonlinear differential equations, ordinary differential equation 324
Nonlinear equations, Numerical examples 137—138 139—140 142—144 147—148 151—152 154—155 158—159 159—160 161—162 162—163 166—167 171—172
Nonlinear equations, roots of Chapter 3 127—186
Nonlinear equations, roots of, Aitken’s acceleration method 145
Nonlinear equations, roots of, Bairstow’s method 164—167
Nonlinear equations, roots of, behavior of nonlinear equations 132—135
Nonlinear equations, roots of, bisection method see “Interval halving”
Nonlinear equations, roots of, bounding roots 130—133
Nonlinear equations, roots of, Brent’s method 169
Nonlinear equations, roots of, closed domain methods 135—140
Nonlinear equations, roots of, comparison of Newton’s method and the secant method 104
Nonlinear equations, roots of, example problem 127—129
Nonlinear equations, roots of, false position 138—140
Nonlinear equations, roots of, fixed-point iteration 141—145
Nonlinear equations, roots of, fixed-point iteration, convergence rate 144—145
Nonlinear equations, roots of, fixed-point iteration, error analysis 144—145
Nonlinear equations, roots of, four-bar linkage example 127—129
Nonlinear equations, roots of, general features of 130—135
Nonlinear equations, roots of, general philosophy of root finding 135
Nonlinear equations, roots of, Graeff’s method 169
Nonlinear equations, roots of, graphing the function 131—132
Nonlinear equations, roots of, incremental search 132
Nonlinear equations, roots of, interval halving 135—138
Nonlinear equations, roots of, introduction to 127—130
Nonlinear equations, roots of, Jenkins — Traub method 169
Nonlinear equations, roots of, Laguerre’s method 169
Nonlinear equations, roots of, Lehmer — Schur method 169
Nonlinear equations, roots of, Muller’s method 141 152—155
Nonlinear equations, roots of, Newton’s method 140 146—150
Nonlinear equations, roots of, Newton’s method for polynomials 158—163
Nonlinear equations, roots of, Newton’s method, approximate method 149
Nonlinear equations, roots of, Newton’s method, complex roots 162—163
Nonlinear equations, roots of, Newton’s method, convergence rate 148—149
Nonlinear equations, roots of, Newton’s method, error analysis 148—149
Nonlinear equations, roots of, Newton’s method, lagged method 149
Nonlinear equations, roots of, open domain methods 140—155
Nonlinear equations, roots of, packages 179
Nonlinear equations, roots of, pitfalls of root finding 167—169
Nonlinear equations, roots of, polishing roots 149 157
Nonlinear equations, roots of, polynomials 155—167
Nonlinear equations, roots of, programs for 173—179
Nonlinear equations, roots of, quotient-difference (QD) method 169
Nonlinear equations, roots of, refining roots 133
Nonlinear equations, roots of, regula falsi see “False position method”
Nonlinear equations, roots of, secant method 150—152
Nonlinear equations, roots of, secant method, convergence rate 152
Nonlinear equations, roots of, Steffensen’s method 145
Nonlinear equations, roots of, summary 179—181
Nonlinear equations, roots of, systems of nonlinear equations 169—173
Nonlinear equations, systems of 169—173
Nonlinear first-order initial-value ODE 338 341—343
Nonlinear first-order initial-value ODE, linearization of 342
Nonlinear functions, least squares fit 234
Nonlinear implicit finite difference equations, boundary-value ODEs 393—396
Nonlinear implicit finite difference equations, boundary-value, Newton’s method 394—396
Nonlinear implicit finite difference equations, boundary-value, time linearization 393—394
Nonlinear implicit finite difference equations, elliptic PDEs 570—571
Nonlinear implicit finite difference equations, elliptic PDEs, iteration method 570
Nonlinear implicit finite difference equations, elliptic PDEs, Newton’s method 571
Nonlinear implicit finite difference equations, hyperbolic PDEs 682
Nonlinear implicit finite difference equations, parabolic PDEs 625—627
Nonlinear implicit finite difference equations, parabolic PDEs, iteration 626
Nonlinear implicit finite difference equations, parabolic PDEs, Newton’s method 626
Nonlinear second-order boundary-value ODEs 438 440
Nonrectangular domains 562—570
Nonrectangular domains, approximate physical boundaries 563
Nonrectangular domains, cylindrical coordinates 563
Nonrectangular domains, nonuniform FDAs 563—568
Nonrectangular domains, spherical coordinates 563
Nonrectangular domains, transformed spaces 563 566 568—570
Nonsmoothly varying problems 350
Nonsymmetrical difference formulas 269—270
Nonuniform FDAs 563—568
Nonuniform grids, boundary value ODEs 477—480
Nonuniform grids, finite element method 731 758
Nonuniform grids, nonequally spaced FDAs 477—478
Nonuniform grids, solution on a nonuniform grid 477—480
Nonuniform grids, transformed uniform grid 477
Normal equations (least squares), higher-degree polynomials 228—230
Normal equations (least squares), multivariate polynomials 232
Normal equations (least squares), straight line 227
Norms 55—58
Norms, definition of 56
Norms, matrix 56
Norms, scalar 56
Norms, vector 56
Notation see “Index notation”
Number representation 5
Numbers 5
Numerical differentiation Chapter 5 251—284
Numerical differentiation, centered differences 260—261 262 263 268
Numerical differentiation, difference formulas 262—264 270—271
Numerical differentiation, direct fit polynomials 255—256
Numerical differentiation, divided difference polynomials 255—256
| Numerical differentiation, equally spaced data 257—264 276—278
Numerical differentiation, error estimation 270 272
Numerical differentiation, example 253
Numerical differentiation, extrapolation 270 272
Numerical differentiation, introduction to 251—254
Numerical differentiation, Lagrange polynomials 255—256
Numerical differentiation, Newton backward-difference polynomial 261—262
Numerical differentiation, Newton forward-difference polynomial 257—261
Numerical differentiation, numerical examples 256—257 259—260 261 264 268 269—270 272
Numerical differentiation, numerical methods, difference formulas 262—264 271
Numerical differentiation, numerical methods, direct fit polynomial 255—256
Numerical differentiation, numerical methods, divided difference polynomial 255—257
Numerical differentiation, numerical methods, known functions 252
Numerical differentiation, numerical methods, Lagrange polynomial 255—256
Numerical differentiation, numerical methods, Newton backward-difference polynomial 261—262
Numerical differentiation, numerical methods, Taylor series approach 264—270
Numerical differentiation, one-sided differences 258 262 263 268
Numerical differentiation, order of approximation 259 267
Numerical differentiation, packages 278—279
Numerical differentiation, programs for 273—278
Numerical differentiation, space derivatives 264—268
Numerical differentiation, summary 279
Numerical differentiation, Taylor series approach 264—270
Numerical differentiation, time derivatives 268—269
Numerical differentiation, truncation error 267
Numerical differentiation, unequally spaced data 254—257 273—276
Numerical diffusion 664—665
Numerical dispersion 664—665
Numerical information propagation speed 455 456
Numerical integration Chapter 6 285—321
Numerical integration, adaptive integration 299—302
Numerical integration, composite formulas 292 294 296
Numerical integration, direct fit polynomials 288—289
Numerical integration, equally spaced data 288—289 290—297
Numerical integration, error control 297—298
Numerical integration, error estimation 297—298
Numerical integration, error, global (total) 292 294 296
Numerical integration, error, local 292 294 296
Numerical integration, example 287
Numerical integration, extrapolation 297—299
Numerical integration, Gaussian quadrature 302—306
Numerical integration, Gaussian quadrature, table of parameters 304
Numerical integration, higher-order Newton-Cotes formulas 296—297
Numerical integration, increment 291
Numerical integration, interval 291
Numerical integration, introduction to 16 285—288
Numerical integration, know functions 286
Numerical integration, multiple integrals 306—310
Numerical integration, Newton — Cotes formulas 290—297
Numerical integration, nonequally spaced data 288—289
Numerical integration, numerical examples 289 292—293 294—295 298—299 300—301 304—306 306—310
Numerical integration, numerical methods, adaptive 299—302
Numerical integration, numerical methods, direct fit polynomial 288—289
Numerical integration, numerical methods, extrapolation 297—299
Numerical integration, numerical methods, Gaussian quadrature 302—306
Numerical integration, numerical methods, multiple integrals 306—310
Numerical integration, numerical methods, Newton forward-difference polynomials 290—297
Numerical integration, numerical methods, Newton — Cotes formulas 290—297
Numerical integration, numerical methods, Romberg integration 297—299
Numerical integration, numerical methods, Simpson’s 1/3 rule 293—295
Numerical integration, numerical methods, Simpson’s 3/8 rule 295—296
Numerical integration, numerical methods, trapezoid rule 291—293
Numerical integration, packages 315
Numerical integration, programs for 310—315
Numerical integration, quadrature 285
Numerical integration, range of integration 291
Numerical integration, rectangle rule 290—291
Numerical integration, Romberg integration 297—299
Numerical integration, Simpson’s 1/3 rule 293—295
Numerical integration, Simpson’s 3/8 rule 295—296
Numerical integration, summary 315—316
Numerical integration, tabular data 286
Numerical integration, trapezoid rule 291—293
Objective of the book 1
ODE, acronym ODE 323
ODE, boundary-value 435—499
ODE, definition of 323
ODE, initial-value 335—433
ODE, stable 341
ODE, unstable 341
ODEs Part II 323—333
ODEs, auxiliary conditions 324 325
ODEs, boundary value Chapter 8 435—499
ODEs, boundary value, boundary conditions 441
ODEs, boundary value, boundary conditions at infinity 441 465—466
ODEs, boundary value, definition of 323 330—332
ODEs, boundary value, derivative BCs, equilibrium method 461—464
ODEs, boundary value, derivative BCs, example problem 458—459
ODEs, boundary value, derivative BCs, shooting method 459—461
ODEs, boundary value, Dirichlet boundary conditions 441
ODEs, boundary value, eigenproblems 480—482
ODEs, boundary value, equilibrium method 438 450—458
ODEs, boundary value, equilibrium method, boundary condition at infinity 463—466
ODEs, boundary value, equilibrium method, boundary condition at infinity, asymptotic solution 466
ODEs, boundary value, equilibrium method, boundary condition at infinity, finite domain 465—466
ODEs, boundary value, equilibrium method, boundary conditions 441
ODEs, boundary value, equilibrium method, compact three-point fourth-order method 467—471
ODEs, boundary value, equilibrium method, consistency 450
ODEs, boundary value, equilibrium method, convergence 450
ODEs, boundary value, equilibrium method, derivative boundary conditions 461—464
ODEs, boundary value, equilibrium method, eigenproblems 480—482
ODEs, boundary value, equilibrium method, eigenproblems, approximate eigenvalues 481—482
ODEs, boundary value, equilibrium method, eigenproblems, exact eigenvalues 480—481
ODEs, boundary value, equilibrium method, eigenproblems, example 481—482
ODEs, boundary value, equilibrium method, extrapolation 453—454
ODEs, boundary value, equilibrium method, finite difference approximations 450
ODEs, boundary value, equilibrium method, finite difference grids 450—451
ODEs, boundary value, equilibrium method, five-point fourth-order method 466—467
ODEs, boundary value, equilibrium method, higher-order methods 466—471
ODEs, boundary value, equilibrium method, mixed boundary condition 464
ODEs, boundary value, equilibrium method, nonlinear boundary-value problems 471—477
ODEs, boundary value, equilibrium method, nonlinear boundary-value problems, iteration 471—474
ODEs, boundary value, equilibrium method, nonlinear boundary-value problems, Newton’s method 474—477
ODEs, boundary value, equilibrium method, numerical examples 451—458 462—464 470—471 473—480
ODEs, boundary value, equilibrium method, numerical methods, compact fourth-order method 467—471
ODEs, boundary value, equilibrium method, numerical methods, extrapolation 453—454
ODEs, boundary value, equilibrium method, numerical methods, five-point fourth-order method 469
ODEs, boundary value, equilibrium method, numerical methods, second-order method 450—453
ODEs, boundary value, equilibrium method, order 450
ODEs, boundary value, equilibrium method, second-order boundary-value problem 450—451
ODEs, boundary value, equilibrium method, summary 488—490
ODEs, boundary value, exact solution of 440 455
ODEs, boundary value, example problem 436—437 455
ODEs, boundary value, general features of 439—441
ODEs, boundary value, higher-order ODEs 440
ODEs, boundary value, introduction to 436—439
ODEs, boundary value, linear second-order ODE 439
ODEs, boundary value, linearization of 472
ODEs, boundary value, mixed boundary conditions 441
ODEs, boundary value, Neumann boundary conditions 441
ODEs, boundary value, nonlinear second-order ODE 438 440 471—477
ODEs, boundary value, nonuniform grids 477—480
ODEs, boundary value, packages 488
ODEs, boundary value, programs for 483—488
ODEs, boundary value, shooting method 438 441—449
ODEs, boundary value, shooting method by iteration 444—447
ODEs, boundary value, shooting method, advantages of 488
ODEs, boundary value, shooting method, boundary condition at infinity 465—466
ODEs, boundary value, shooting method, boundary condition at infinity, asymptotic solution 466
ODEs, boundary value, shooting method, boundary condition at infinity, finite domain 465—466
ODEs, boundary value, shooting method, boundary conditions 441
ODEs, boundary value, shooting method, concept 441—442
ODEs, boundary value, shooting method, consistency 442
ODEs, boundary value, shooting method, convergence 442
ODEs, boundary value, shooting method, derivative boundary conditions 458—461 464—466
ODEs, boundary value, shooting method, disadvantages of 489
ODEs, boundary value, shooting method, extrapolation 448—449
ODEs, boundary value, shooting method, fourth-order Runge — Kutta method 446—447
ODEs, boundary value, shooting method, higher-order methods 466
ODEs, boundary value, shooting method, higher-order ODEs 449
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