Butcher J. — Numerical Methods for Ordinary Differential Equations :: Электронная библиотека попечительского совета мехмата МГУ

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Butcher J. — Numerical Methods for Ordinary Differential Equations

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Название: Numerical Methods for Ordinary Differential Equations

Автор: Butcher J.

Аннотация:

Researchers and students from numerical methods, engineering and other sciences will find this book provides an accessible and self-contained introduction to numerical methods for solving ordinary differential equations. It stands out amongst other books on the subject because of the author's lucid writing style, and the integrated presentation of theory, examples, and exercises.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 440

Добавлена в каталог: 09.07.2005

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Предметный указатель

$A(\alpha)$ -stability      212—213
$\Phi$ -equivalence      264
A-stability      71 212 221 244 252 255 310 326 336 340 348 382 395
Adams, J.C.      xii 98 359
Alexander, R.      244
Algebraic analysis of order      389
AN-stability      228 235
Annihilation condition      401 403
Arithmetic-geometric mean      36
Axelsson, O.      222
B-series      263
B-stability      233
Barrier, Dahlquist first      335—337 339 364
Barrier, Dahlquist second      342
Barrier, Daniel — Moore      385
Barrier, Ehle      223 226 227
Barrier, explicit Runge — Kutta      258
Barton, D.      108
Bashforth, F.      xii 8 359
BN-stability      233—235
Boundary locus      328 329
Brenan, K.E.      xiii
Brouder, C.      263
Burrage, K.      118 241 249 357
Butcher — Chipman conjecture      386
Butcher, J.C.      86 116 118 149 175 181 222 223 241 244 249 254 260 263 284 341 357 364 366 386 393 394 400 405 410
Byrne, G.D.      115 364
Calvo, M.P.      xiii
Campbell, S.L.      xiii
Cash, J.R.      254
Cauchy — Schwarz inequality      52
Chartier, P.      405
Chipman, F.H.      249 386
Christoffel — Darboux formula      251
Coefficient tableau      87
Companion matrix      25
Compensated summation      75 76
Conjugacy      285
Consistency      100 102 301 304—306 308 310 369 373 374 380
Contraction mapping principle      23
Convergence      63 100 102 301 303 306 308 310 369 371 372 374 380
Convolution      30
Cooper, G.J.      179
Covariance      101 370
Curtis, A.R.      179
Curtiss, C.F.      98
Dahlquist, G.      98 230 231 304 336 342—344 346—348 363
Daniel, J.W.      385
DASSL      xiii
Davis, P.J.      20
Density of tree      126
Derivative weight      142
Difference equation      31
Difference equation, Fibonacci      33
Difference equation, linear      31 37
Differential algebraic equation      xii
Differential equation, autonomous      2 135
Differential equation, chemical kinetics      15
Differential equation, dissipative      11
Differential equation, Hamiltonian      xiii 3
Differential equation, harmonic oscillator      17
Differential equation, initial value problem      2
Differential equation, Kepler      4 79 120
Differential equation, linear      25
Differential equation, Lotka — Volterra      18
Differential equation, many-body      7
Differential equation, method of lines      9
Differential equation, mildly stiff      54
Differential equation, Prothero and Robinson      246
Differential equation, restricted three-body      8
Differential equation, Robertson      16
Differential equation, simple pendulum      13
Differential equation, stiff      26 27 58 68 228 291 296 326 336
Differential equation, van der Pol      17
Differentiation      131
DIFSUB      xii
Dirichlet conditions      10
DJ-reducibility      230
Donelson, J.      364
Dormand, J.R.      181 194
Doubly companion matrix      405 410
E-polynomial      214 253
Effective order      256 285 348 405
Efficient extrapolation      282
Ehle conjecture      see "Barrier Ehle"
Ehle, B.L.      222 223 228
Elementary differential      134 136 141
Elementary differential, independence      146
Elementary weight      140 142
Elementary weight, independence      149
Elliptic integral      36
EQUIVALENCE      264
Error, asymptotic formula      66
Error, constant      318
Error, estimation      72 181
Error, global truncation      61 152 153 248 317 374 379
Error, growth      319
Error, local estimation      85 184 374 393
Error, local truncation      55 60 65 66 72 105 151 153 181 292 308 317 319 377 401
Error, per step      293
Error, per unit step      293 294
Error, rounding      74
Euler, L.      45
Existence and uniqueness      23
Fehlberg, E.      181 191
Feng Kang      xiii
finger      72 224
Forest      270
Forest product      270
FSAL property      194 360
G-stability      326 343 344 348
Gaussian quadrature      198 261
Gear, C.W.      xii 116 302 350 352 364
Generalized order conditions      172
Generalized Pade approximation      384
Gibbons, A.      108
Gill — Moller algorithm      75 76
Gill, S.      75 86 167
Gragg, W.B.      116 364
Graph      123
Gustafsson, K.      295 296
Hairer, E.      xii xiii 72 147 179 202 223 250 260 263 339 341
Hamiltonian      5
Hansen, E.      364
Henrici, P.      75 98
Heun, K.      86
Higham, N.J.      75
Hirschfelder, J.O.      98
Homomorphism      272
Hundsdorfer, W.H.      344
Huta, A.      86 149 175 177
Ideal      283
implementation      242
Internal order      169
Internal weight      142
Iserles, A.      xiii 224
Jackiewicz, Z.      393 400
Jacobian matrix      xii 28 243 254 296
Jeltsch, R.      230 231
Kahan, W.      75
Kirchgraber, U.      322
Kronecker product      358
Kutta, W.      86 164 174
L-stability      244 245 252 382
Labelled trees      131
Laguerre polynomial      250—252
Lambert, J.D.      304
Lambert, R.J.      115 364
Laplace transform      28
Legendre polynomials      198

Leone, P.      241
Limit cycles      17
Lipschitz condition      23 59
Lobatto quadrature      179 205
Local extrapolation      181
Lotka, A.J.      18
Lubich, C.      xiii 202
Lundh, M.      295
Matrix, convergent      39
Matrix, Jordan      40
Matrix, power bounded      39
Matrix, stable      39
Merson, R.H.      86 181 184
Method, Adams — Bashforth      xii 98 102 104 302 315 329 362
Method, Adams — Moulton      xii 84 98 102 104 314 362
Method, adjoint      202
Method, Almost Runge — Kutta      366 367 400
Method, backward difference      98 314 316
Method, collocation      236
Method, cyclic composite      364
Method, DESIRE      256 257
Method, diagonally implicit      244
Method, DIMSIM      xii 367 394 395
Method, DIMSIM types      395
Method, DIRK      244 395
Method, Dormand and Prince      181 194
Method, Euler      xi 45 59 72
Method, Euler convergence      62
Method, Euler order of      63
Method, Fehlberg      181 191
Method, Gauss      221 237 240 248
Method, general linear      xii 83 117 357—413
Method, general linear order of      263
Method, generalized linear multistep      117
Method, Gill      167
Method, higher derivative      82 112
Method, Huta      149 175
Method, hybrid      115 364
Method, implicit      83
Method, implicit Euler      57 58
Method, implicit Runge — Kutta      94
Method, IRK stable      409
Method, Kutta      174
Method, leapfrog      322
Method, linear multistep      xii 81 97 99 301—355 361
Method, linear multistep implementation      349
Method, linear multistep order of      312
Method, Lobatto IIIA      84 360
Method, Lobatto IIIC      221 240 248
Method, Merson      181 184
Method, mid-point rule      87
Method, modified multistep      116
Method, multiderivative      82
Method, multistage      82 357
Method, multistep      82
Method, multivalue      82 357
Method, Nordsieck      350 353
Method, Nystroem      98
Method, Obreshkov      82 385
Method, one-leg      343 344 347 363
Method, predictor-corrector      xii 85 98 102 104 333 362
Method, pseudo Runge — Kutta      115 116 364 365
Method, Radau IA      221 240 248
Method, Radau IIA      221 237 240 248
Method, reflected      202
Method, Rosenbrock      83 113
Method, Runge — Kutta      xi xii 79 86 105 123—299 302 360
Method, Runge — Kutta algebraic property      262
Method, Runge — Kutta class      263 268
Method, Runge — Kutta effective order of      287
Method, Runge — Kutta embedded      185
Method, Runge — Kutta equivalence class      263 268
Method, Runge — Kutta explicit      156
Method, Runge — Kutta generalized      275 391
Method, Runge — Kutta group      266
Method, Runge — Kutta identity      268
Method, Runge — Kutta implementation      290
Method, Runge — Kutta implicit      92 196 242
Method, Runge — Kutta inverse      268
Method, Runge — Kutta irreducible      264
Method, Runge — Kutta order of      147
Method, SDIRK      395
Method, singly-implicit      249 251 252
Method, starting      105 302 388
Method, Taylor series      82 107
Method, underlying one-step      320 321 392
Method, Verner      181 193
Method, weakly stable      322
Milne device      104
Milne, W.E.      98 105 322
Moir, N.      405
Moller, O.      75
Moore, R.E.      108 385
Moulton, F.R.      xii 98
Munthe-Kaas, H.Z.      xiii
Neumann conditions      10
Newton iteration      35 85 197 291 296
Nordsieck vector      409
Nordsieck, A.      350 359
Normal subgroup      283
Norsett, S.P.      xiii 72 147 223 244 250 339 341
Nystroem, E.J.      86 98 174
Obreshkov, N.      82
One-sided Lipschitz condition      25 27
Optimal stepsize sequence      181 291
Order      312 387
Order arrow      225 226 341 386
Order barrier      258
Order condition      88 147
Order condition, scalar problems      148
Order star      72 223 224 339 386
Order web      226
P-equivalence      264
Pade approximation      112 215 227
Periodic orbit      18
Perturbing method      285
Petzold, L.R.      xiii
PI control      295
Picard iteration      140
Picel, Z.      222
Powers of matrix      39
Preconsistency      100 304 369
Prince, P.J.      181 194
Prothero, A.      245
Quotient group      283
Rabinowitz, P.      20
Radau code      xii
Radau quadrature      205
Reduced method      230
Relaxation factor      297
Richardson, L.F.      181
Riemann surfaces      339
Robertson, H.H.      16
Robinson, A.      245
Roche, M.      xiii
Romberg, W.      182
Rooted tree      88—90 123
Rooted tree, order of      126
Rosenbrock, H.H.      83 113
Runge — Kutta group      269
Runge, C.      86
Safety factor      293
Sanz-Serna, J.M.      xiii
Scherer, R.      202
Schur criterion      328 332
SDIRK      244
Shampine, L.F.      222
Sheikh, Q.M.      344
Similarity transformation      298
Simplifying assumption      157

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