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Ascher U.M., Russell R.D., Mattheij R.M. — Numerical Solution of Boundary Value Problems for Ordinary Differential Equations
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Название: Numerical Solution of Boundary Value Problems for Ordinary Differential EquationsАвторы: Ascher U.M., Russell R.D., Mattheij R.M.Аннотация: This book is the most comprehensive, up-to-date account of the popular numerical methods for solving boundary value problems in ordinary differential equations. It aims at a thorough understanding of the field by giving an in-depth analysis of the numerical methods by using decoupling principles. Numerous exercises and real-world examples are used throughout to demonstrate the methods and the theory. Although first published in 1988, this republication remains the most comprehensive theoretical coverage of the subject matter, not available elsewhere in one volume.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1995Количество страниц: 595Добавлена в каталог: 31.01.2010Операции: Положить на полку |
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Adam’s scheme 70 Adjoint 270 Adjoint operator 270 Adjoint, self- 97 270 Admissible transformation (of coordinates) 373 Affine invariant 329 Almost block diagonal matrix 308 Alternate row and column, elimination 310 Alternate row and column, pivoting 310 Angles between matrices 38 Angles between subspaces 38 119 Arclength 494 498 Asymptotic expansion 404 Asymptotically equidistributing 364 B-spline 61 260 Backsubstitution 424 Backward differentiation formulas 74 Backward error analysis 46 Backward Euler scheme 74 139 215 433 Banded matrix 43 304 308 Bandwidth 43 Basis, B-spline 61 Basis, Hermite type 59 60 Bc see “Boundary condition” BDF 74 Bifurcation 490 Bifurcation point 493 Bifurcation, Hopf 496 Bifurcation, pitchfork 495 Bifurcation, primary 494 Bifurcation, secondary 494 Bifurcation, transition 495 Block banded matrix 304 Block diagonal matrix (almost) 308 Block tridiagonal matrix 312 Boundary condition (BC) 3 5 Boundary condition (BC), multipoint 6 92 323 470 512 Boundary condition (BC), nonseparated 5 470 Boundary condition (BC), partially separated 5 Boundary condition (BC), scaling of 114 Boundary condition (BC), separated 5 Boundary condition (BC), special point 471 Boundary condition (BC), two point 2 Boundary layer 8 Boundary value problem (BVP) on infinite intervals 483 486 Boundary value problem (BVP) with oscillatory modes 500 Boundary value problem (BVP) with parameters 322 470 Boundary value problem (BVP), discrete 288 Boundary value problem (BVP), first order formulation 3 Boundary value problem (BVP), multipoint 6 Boundary value problem (BVP), singular (first kind) 484 Boundary value problem (BVP), singular (second kind) 478 480 Boundary value problem (BVP), singularly perturbed 113 386 Boundary value problem (BVP), standard form 469 Box scheme 191 Branch 491 Branch switching 499 Branching 493 Broyden update 52 Butcher array 69 BVP 1 Cauch — Schwartz inequality 77 Characteristic polynomial 32 Classical continuation 347 Classical turning point 393 Closure 297 code design 515 Collocation 210 218 222 247 Collocation for high order DE 244 251 Collocation matrix 252 260 Collocation point 210 248 Collocation solution 218 Collocation using splines 259 Collocation, conditioning of 252 Compactification 153 Compactification for a decoupled system 158 316 Compactification, stable 316 Companion matrix 32 complexity 31 35 303 Composite formulas 66 Cond (A) 39 Condensation of parameters 212 307 Condensing method 153 306 Condition number 39 78 81 Conditioned (of BVP), ill 79 94 Conditioned (of BVP), well 79 94 Conditioned (of matrices), ill 39 114 Conditioned (of matrices), well 39 114 Conditioned (of problem), ill 29 Conditioned (of problem), well 29 Conditioning constant 78 95 111 Conjugate transpose 34 Consistency (of difference methods) 71 188 Consistency (of difference methods) of BVP 198 199 Consistency (of difference methods) of IVP 71 Consistency (of difference methods) order 71 Consistency (of fundamental solutions) 280 281 290 Consistency (of fundamental solutions) constant 281 290 Consistency requirement (for reduced solution) 404 Consistent DAE 475 Continuation 344 Continuation with incremental load 347 Continuation, classical 347 Continuation, parameter 490 Continuous decoupling 279 282 Contraction mapping 49 50 Convergence (of difference methods) of BVP 189 205 255 451 Convergence (of difference methods) of IVP 71 Convergence (of difference methods), super- 211 Convergence (of iteration), global 328 332 Convergence (of iteration), linear 49 Convergence (of iteration), local 328 Convergence (of iteration), quadratic 49 Convergence (of iteration), rate of 48 Convergence (of iteration), superlinear 52 Convergent of orderp 71 189 190 199 Criterion function 334 D-stability 442 DAE 474 504 Damped Newton 329 Damping factor 330 Davidenko equation 350 Decomposition 319 Decomposition, almost block 308 Decomposition, LU 40 320 Decomposition, QU 35 43 Decoupling 157 Decoupling algorithm, continuous case 284 Decoupling algorithm, discrete case 291 321 Decoupling, continuous 279 282 Decoupling, discrete 288 Defect correction 234 Defective eigenvalues 33 Deferred correction 228 235 238 240 Delay differential equation 506 Descent direction 330 Diagonally dominant 42 Diagonally dominant, essentially 410 Diagonally dominant, strictly 107 120 Diagonally dominated 410 Dichotomic fundamental solution 118 280 Dichotomy 115 280 289 Dichotomy, discrete case 289 Dichotomy, exponential 116 Dichotomy, ordinary 116 Difference operator 188 Difference operator (positive) 436 Difference scheme (explicit) 69 Difference scheme (implicit) 69 Difference scheme (one step) 68 Difference, finite (method) 185 Differential algebraic equation 474 504 Differential operator 93 188 Discrete BVP 288 305 354 Discrete decoupling 288 Discrete fundamental solution 289 Discrete Green’s function 138 Discretization error 29 Divided differences 56 Dominant (strictly diagonally) 107 120 Effective singularity 339 Eigenvalue 32 Eigenvalue problem (ODE) 478 Eigenvalue, defective 33 Eigenvalue, generalized (problem) 480 Eigenvalue, kinematic 105 Eigenvector 32 Elementary hermitian matrix 43 Elementary lower triangular matrix 40 Elementary reflector 43 Elimination, alternate row-column 310 Elimination, block tridiagonal 313 Elimination, column 310 Elimination, Gaussian 39 Elimination, row 310 Equidistributing mesh 62 363 Equidistribution 62 362 Equilibration 42 Error analysis 28 Error analysis (backward) 46 Error control (IVP) 74 Error equidistribution 362 Error per unit step control 75 Error, discretization 29 Error, global 30 Error, input 30 Error, local 30 72 81 Error, rounding 30 Error, truncation 29 Euler backward 424 Euler’s method 29 68 424 Exact line search 331 Expansion, asymptotic 404 Expansion, matched asymptotic 405 Exponential, dichotomy 389 Exponential, fitting 454 Extrapolation 228 230 Factorization 33 40 Factorization Fehlberg schemes 69 Factorization methods 298 319 Finite difference method 185 Finite element method 266 Fixed point 49 Fixed Point Iteration 49 FLOP 42 Forward substitution 42 Frtchet derivative 53 Function, criterion 334 Function, monitor 363 Function, objective 330 Functional differential equation 505 Fundamental solution (matrix) 86 Fundamental solution (matrix), dichotomic 118 280 Fundamental solution (matrix), discrete 289 Galerkin’s method 271 Gauss formulas 64 Gauss Newton 340 Gauss — (Legendre) points 65 215 Gaussian elimination 39 Gaussian, quadrature 64 Generalized solution 268 Gershgorin 33 268 Gib 37 Global discretization error 29 Global error 71 256 Global method 185 Grade of a vector 33 Gram — Schmidt 34 Greatest lower bound 37 Green’s function 94 Green’s function, discrete 138 Green’s function, first order system 94 95 Green’s function, high order ODE 96 Grid staggered 246 Hermite type basis 59 60 260 Hessenberg form 46 High order schemes 208 Highly oscillatory BVP 500 Homotopy path 344 490 Hopf bifurcation 496 Hyperbolic splitting 401 Ill-conditioning 29 39 79 94 114 Imbedding in a time dependent problem 350 Imbedding, invariant 164 167 Imbedding, parameter 165 Index of DAE 474 478 Infinite interval BVP 483 486 Initial layer 398 Initial value methods 68 457 Initial value problems 2 67 85 Inner solution 390 404 Interpolation 55 Interpolation, Lagrange form 56 Interpolation, Newton form 57 Interpolation, osculatory 58 Interpolation, polynomial 55 Interpolation, spline 62 Invariant imbedding 164 Isolated solution 91 IVP 2 67 85 Jacobian (matrix) 90 109 Jordan block 33 102 Jordan canonical form 33 102 Kinematic eigenvalue 105 Kinematic similarity 105 Lagrange form 56 Layer region 409 443 Layer, boundary 386 398 Layer, initial 398 Layer, interior 386 Layer, shock 394 396 Layer, transition 393 Least squares 45 Least, upper bound 37 Legendre polynomial 65 Limit point 49 Line search, exact 331 Line search, weak 331 Lines (method of), longitudinal 509 Lines (method of), transverse 509 Liouville normal form 481 Lipschitz condition 88 Lipschitz constant 85 Lipschitz continuous 85 Lobatto points 66 215 Local error 72 Local representation 59 Local support (discretization) 61 259 Local truncation error 71 204 Longitudinal method of line 509 LU decomposion 40 320 Lub 37 Lyapunov equation 109 289 Machine epsilon 29 Marching technique 146 155 Marquardt algorithm 340 Matched asymptotic expansion 405 409 Matrix norm 37 Matrix, collocation 252 260 Matrix, companion 32
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