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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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Matrix, diagonally dominant 42 Matrix, elementary lower triangular 40 Matrix, hermitian 43 Matrix, Hessenberg 46 Matrix, orthogonal 33 Matrix, permutation 41 Matrix, positive definite 35 Matrix, staircase 304 306 Matrix, strictly diagonally dominant 42 107 120 Matrix, totally positive 62 Matrix, upper triangular 34 Matrix, Vandermonde 56 Maximizing vector 37 Mesh independence principle 354 Mesh selection 358 381 444 Mesh, equidistributing 363 Mesh, locally almost uniform 451 Mesh, optimal 359 Mesh, quasi uniform 227 361 Mesh, staggered 246 Method of lines 508 Midpoint rule 64 Midpoint scheme 70 73 191 215 Milrch (stabilized) 61 163 Minimizing vector 37 Mixed order system 3 Modes 104 Modes, fast 116 276 392 Modes, slow 116 276 392 Modified Euler 69 Monitor function 363 376 Monomials, B-spline representation 59 Monomials, Hermite type representation 59 Moore — Penrose pseudo inverse 36 Multiple shooting 145 Multiple shooting, standard 146 147 175 Multiple shooting, theoretical 415 418 Multiple solution 490 Multiplicity, algebraic 33 Multiplicity, geometric 33 Multipoint BVP 92 512 Multistep method 70 Newton direction 329 338 Newton method 48 176 195 327 335 Newton — Cotes formulas 64 Newton — Kantorowich 51 Newton, damped 329 Newton, modified 341 Newton, quasi 51 52 Nonlinear equations 48 Nonseparated BC 5 470 Norm 36 37 Norm, 1- 37 Norm, 2- 37 Norm, Euclidean 37 Norm, function 77 Norm, Hoelder 35 Norm, induced 37 Norm, matrix 37 Norm, max 37 Norm, Sobolev 77 Norm, sup 37 79 Norm, vector 36 Normal equation 45 Objective function 330 One sided schemes 116 One step schemes 68 Operator, boundary 93 Operator, difference 188 Operator, differential 93 188 Ordinary dichotomy 116 Ordinary differential equation (ODE) 3 Ordinary differential equation (ODE) inhomogeneous 3 Ordinary differential equation (ODE), delay 506 Ordinary differential equation (ODE), first order 3 Ordinary differential equation (ODE), functional 505 Ordinary differential equation (ODE), generalized 474 Ordinary differential equation (ODE), high order 3 244 470 Ordinary differential equation (ODE), homogeneous 3 Ordinary differential equation (ODE), mixed order 4 Ordinary differential equation (ODE), nonlinear 3 Orthogonal, Matrix 33 Orthogonal, projection 36 117 Orthogonalization 33 43 Orthonormal polynomial 64 Oscillatory (highly) 500 Osculatory interpolation 58 Outer solution 390 404 Parameter(s), BVP with 322 470 Parameter(s), condensation of 212 261 307 Parameter(s), imbedding 165 Partial pivoting 41 308 Partially separated 5 Path Finder 4 58 Path following 490 496 Path, homotopy 344 PDE 508 Petrov — Galerkin 271 Piecewise polynomial 59 218 Pitchfork bifurcation 495 Pivot 41 Pivoting, alternate row and column 310 Pivoting, column 310 Pivoting, partial 41 308 Pivoting, row 310 Polychotomy 514 Polynomial, interpolation 55 Polynomial, orthonormal 64 Polynomial, piecewise 59 Positive definite symmetric 35 Precision of quadrature 64 211 Predictor-correct (Newton) 334 Preprocessing 237 Primary bifurcation 64 211 Principal error function 227 Principal vector 33 Projection (orthogonal) 36 125 Pruefer transformation 481 Pseudo-arclength 498 Pseudo-inverse 36 340 QR aigorithmn 45 QU decomposition 35 Quadrature 63 Quadrature rule 63 Quadrature, composite formulas 66 Quadrature, Gauss point 65 Quadrature, Gaussian 64 Quadrature, Lobatto point 66 Quadrature, precision of 64 211 Quadrature, Radau point 55 Quasi Newton algorithm 51 52 Quasi uniform mesh 227 361 Quasilinearization 53 222 Rank-1 update 52 343 Rate of convergence 48 Rayleigh quotient 35 Recursion backward 312 Recursion forward 312 Reduced equation 411 413 Reduced solution 390 451 Reduced superposition 143 Reflection 33 43 Reimbedding 168 Representation, global 59 Representation, local 59 Riccati differential equation 165 166 Riccati method 64 167 460 Riccati transformation 166 392 Richardson extrapolation 228 Ritz method 267 Rotation 33 Roundoff (error) 29 Runge — Kutta 68 210 Runge — Kutta representation 252 Runge — Kutta scheme 213 Runge — Kutta, explicit 210 Runge — Kutta, implicit 210 Runge — Kutta, k-stage 210 Scaling of BC 114 Scheme, higher order 208 Scheme, one-sided 432 Scheme, symmetric 440 schur 35 Secondary bifurcation 494 Segmentation 397 410 423 Separated BC 5 Sequential shooting 457 Shift 45 Shock layer 394 396 shooting 133 Shooting, bidirectional 178 Shooting, multiple 145 175 Shooting, sequential 457 Shooting, simple 91 Shooting, single 91 137 170 Shooting, standard multiple 146 147 Similar 32 Similarity transformation 32 Similarity, kinematic 105 Singular BVP (first kind) 450 484 Singular BVP (second kind) 478 480 Singular perturbation 386 Singular point 490 498 Singular value 35 Singular value decomposition (SVD) 35 Singularity (essential) 339 Singularly perturbed BVP 113 386 Singularly perturbed IVP 112 116 Singularly perturbed, singular 403 Sobolev Norm 77 Solution, collocation 218 Solution, consistent (fundamental) 280 281 290 Solution, fast 392 Solution, fundamental 86 Solution, generalized 268 Solution, highly oscillatory 500 Solution, inner 390 404 Solution, isolated 91 Solution, multiple 490 Solution, outer 390 404 Solution, reduced 390 Solution, slow 392 Solution, weak 268 Spectral radius 32 SPLINE 59 Spline, B- 61 Spline, Hermite 59 Spline, smooth 59 Stability constant 81 265 Stability of bifurcation 493 Stability of block methods 318 Stability of collocation 262 Stability of decoupling 385 Stability of finite difference methods 200 201 Stability of initial value problems 99 100 Stability of multiple shooting 149 Stability of single shooting 137 Stability, 74 Stability, A- 73 Stability, algebraic 73 Stability, AN- 73 Stability, asymptotic 100 Stability, di(chotomic) 458 Stability, L- 74 Stability, relative 100 Stability, uniform 100 Stabilized march 161 163 Staggered mesh 246 Staircase matrix 304 306 Standard form 469 Steepest descent 334 340 Stiff 73 286 387 Stiff decay 74 Stretching transformation 387 415 428 Strictly diagonally dominant 107 120 Sturm — Liouville 480 Substitution, back 42 Substitution, forward 42 Superconvergence 221 Superconvergence Order 255 Superposition 135 Superposition, reduced 143 SVD 35 Symmetric positive definite 35 Symmetric schemes 440 Time scales 392 Tolerance 31 Totally positive matrix 62 Transformation methods 373 Transformation, admissible 373 Transformation, elementary 40 Transformation, Householder 43 Transformation, reflection 33 Transformation, rotation 34 Transformation, similarity 32 Transformation, stretching 386 Transient 388 Transition bifurcation 495 Transition layer 393 396 Tranverse method of lines 509 Trapezoidal scheme 190 196 215 Tridiagonal matrix 187 Truncation (error) 71 188 199 204 Turning point for singularly perturbed problem 393 396 442 Turning point, singular point 491 496 Unitary 34 Update (rank 1-) 52 Upstream 434 Upwind 434 Vandermonde matrix 56 Variational equation 109 Variational formulation 267 Variational problem 90 Vector, grade of 33 Vector, maximizing 37 Vector, minimizing 37 Vector, principal 33 Weak line search 331 Weak solution 268 Weight function 331 Well-conditioning 39 79 94 114 wronskian 98
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