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Ascher U.M., Russell R.D., Mattheij R.M. — Numerical Solution of Boundary Value Problems for Ordinary Differential Equations
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 Equations

Авторы: 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.

Many problems, arising in a wide variety of application areas, give rise to mathematical models which form boundary value problems for ordinary differential equations. These problems rarely have a closed form solution, and computer simulation is typically used to obtain their approximate solution. This book discusses methods to carry out such computer simulations in a robust, efficient, and reliable manner.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1995

Количество страниц: 595

Добавлена в каталог: 31.01.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
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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