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Mattheij R.M.M., Molenaar J. — Ordinary Differential Equations in Theory and Practice (Classics in Applied Mathematics) (No. 43)
Mattheij R.M.M., Molenaar J. — Ordinary Differential Equations in Theory and Practice (Classics in Applied Mathematics) (No. 43)

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Название: Ordinary Differential Equations in Theory and Practice (Classics in Applied Mathematics) (No. 43)

Авторы: Mattheij R.M.M., Molenaar J.

Аннотация:

In order to emphasize the relationships and cohesion between analytical and numerical techniques, Ordinary Differential Equations in Theory and Practice presents a comprehensive and integrated treatment of both aspects in combination with the modeling of relevant problem classes. This text is uniquely geared to provide enough insight into qualitative aspects of ordinary differential equations (ODEs) to offer a thorough account of quantitative methods for approximating solutions numerically and to acquaint the reader with mathematical modeling, where such ODEs often play a significant role.

Originally published in 1995, the text remains timely and useful to a wide audience. It provides a thorough introduction to ODEs, since it treats not only standard aspects such as existence, uniqueness, stability, one-step methods, multistep methods, and singular perturbations, but also chaotic systems, differential-algebraic systems, and boundary value problems. The authors aim to show the use of ODEs in real life problems, so there is an extended chapter in which not only the general concepts of mathematical modeling but also illustrative examples from various fields are presented. A chapter on classical mechanics makes the book self-contained.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Revised edition

Год издания: 2002

Количество страниц: 405

Добавлена в каталог: 28.10.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Acceleration      281
Adams      192 225
Adams — Bashforth formula      173 189
Adams — Moulton formula      173 189
Adhesive forces      369
Applied force      283 324
Asymptotic analysis      304
Asymptotic expansion      61 207
Asymptotic method      211
Attractor      151
Autonomous      9
Autoregressive predictor      166
Backward difference      17 381
Backward Differences Formula (BDF)      174
Banach space      32
Basin of attraction      110 151 344
BDF family      222
Bead      3
Bead-on-a-hoop      301
Bifurcation      152 372
boundary conditions      257
Boundary layer      202
Boundary value problem (BVP)      8 257
Box-Counting Dimension      374
Box-counting method      153 157
Brakes      305
Buckingham's theorem      308
Butcher matrix      52
Butterfly of Lorenz      140
Canonical form of matrix      101
Cantor set      159 160
Capacitor      200 232 351
Capacity      157 352 374
catalyst      204
Cauchy problems      4
Cauchy sequence      32
Cauchy — Peano theorem      30
Centre      101
Centrifugal force      325
Centripetal force      325
Chaos theory      137
Chaotic attractor      150 152 372
Chaotic system      137
Characteristic exponents      90
Characteristic multipliers      90 365
Characteristic polynomial      18
Classical mechanics      279
Clutch      305
Collocation methods      275
Companion matrix      15 178
Complementary error function      315
Compressors      360
Configuration space      283
Conservative system      150 287
Conserved quantity      289
Consistency      20 54 305
Consistency order      54
Continuation of local solutions      34 35
Continuation theorem      35
Contractive mapping principle      32 396
Contractivity      220
Convergence      59
Corrector      186
Correlation dimension      159
Correlation function      158
Crank shaft      360
Critical point      7
D'Alembert, principle of      283
Dahlquist barrier      177 219
Damped Newton method      271
Damping      95
Degrees of freedom      283
Dichotomy      262
Difference equations      15
Differential index      238
Differential-algebraic equations      323
DIFSUB      223
Dimensional analysis      307
Direct method      121
Direction field      5
Dirichlet conditions      258
Discretisation      18
Dissipative system      150
Domain of attraction      110
Double deck systems      204
Doubling map      138 144 148 152 169
Drift      250
Drift problem      234
Dripping faucet      368
Dynamical systems      137
Dynamics      138
Electric circuit      200 352
Electrical network      232
Electromagnetic force      282
Elliptic integral      296
Elliptic point      292
Embedding dimension      163
Embedding procedure      65 163
Embedding space      163
Embedding theorem      163
Energy      290
Engine      363
Epidemic      338
Equations of motion      281
Equilibrium point      7
Equivalence principle      281
Ergodic system      153
Error constant      176
Error Per Step (EPS)      65
Error Per Unit Step (EPUS)      65
Essential root      177
Euler backward      53 338
Euler forward      19 52 335
Euler — Lagrange equations      288
Euler — Lagrange formalism      323
Evolution      257
Evolution matrix function      83 102 103
Evolution problems      4
Existence interval      34
Existence, global      36
Existence, local      31
Exponential divergence      39 143
Exponential fitting      230
Exponential integral      206
Extrapolated global error estimate      62
Fehlberg procedure      71
Feigenbaum constant      139
fibonacci      18
Fisher model      355 360
Fitzhugh — Nagumo model      352 360
Fixed point      7
Floquet theorem      90 365
Fly-wheel      360
Focus      101
Forward difference      17
Fourier series      91
Fourier spectrum      366
Fractal dimension      157
Fredholm alternative      259
Friction      282
Froude number      313
Functional matrix      4
Fundamental solution      83
Gaussian elimination      397
Gaussian quadrature      56 381
Gear procedure      223
Generalised Cantor set      168
Generalised coordinates      285
Generalised velocities      285
Givens' method      397
Global discretisation error      57
Global error      180
Global error function      60 184
Global existence theorem      80
Global nature of solution      258
Gram — Schmidt process      151 397
Gravitation      281
Green's matrix      260
Gronwall, Lemma of      28
Group properties      12
Hamiltonian      288
Hamiltonian formalism      288 324
Harmonic force      282
harmonic oscillator      3 94 96
Hausdorff dimension      158
Heat diffusion      313
Henon map      139 145 149 153 167
Hermite interpolation      56 58 379
Hessenberg form      240
Heteroclinic orbit      293
Heun's method      53
Heun's second order method      75
Heun's third order method      75
Hidden constraints      242
Higher order ODE (HODE)      13
Holonomic constraints      283
Homoclinic orbit      293
Hooke's law      282
Horizontal isocline      125
Householder's method      397
Hyperbolic attractor      156
Hyperbolic point      119 292
Immune system      342
implementation      304
Increment function      214
inductor      351
Inertial frames      280
Infinitesimal generator      12
Influenza      342
Information dimension      159
Initial value problem (IVP)      2 4
Inner solution      208
Instability      110
Integral equation (Volterra)      7
Integral motion      4 15
Invariant measure      153
Invariant set      7
Inverse resonance      321
Invertible map      153
Isoclines      125
Isolated solution      261
Iteration function      138
Jacobian matrix      4
Jordan block      87 387
Jordan curve      128
Jordan form of matrix      86 387 388
Kinematic constraints      282 323
Kirchhoff's laws      232
Kirchhoff's laws, first law      353
Kirchhoff's laws, second law      200
Koch curve      168
Korteweg and De Vries      330
Lagrange coordinates      286
Lagrange interpolation      379
Lagrange multipliers      248 283 322
Lagrangian      287
Layer      200
Linear independence      82
Linear multistep method      172
Linear vector space      82
Linearisation      46 116
Liouville transformation      92 364
Liouville's theorem      290
Lipschitz constant      27
Lipschitz continuity      27
LMM      172
Local discretisation error      20 54 174
Local divergence      141
Local error function      60
Local existence theorem      31
Logistic map      139 152
Lorentz force      282
Lorenz equations      140 145 149 153
Lyapunov exponents      146
Lyapunov function      121
Magnified error      185
Mass-spring system      369
Matched asymptotic expansion      207
Matrix decompositions      397
Matrix pencil      234
Maxwell equations      305
Measure      153
Membrane      351
Midpoint rule      176
Milne's device      189
Modified Euler method      75
Modified Newton method      225
Modular approach      306
Moment of inertia      362
Momentum      280
Multiple shooting      272
Multipoint conditions      8
Multistep prediction      165
MUSN      274
Nagumo model      357 359
Natural measure      154
Navier — Stokes equations      305
Nerve membrane      351
Neumann conditions      258
Newton — Cotes formula      53
Newton — Kantorovich theorem      270
Newton's first law      3 280
Newton's second law      2 280
Newton's Third Law      281
Nilpotency index      236
Node      99 102
Non-dimensionalisation      304
Non-invertible map      153
Nordsieck vector      191
Norm, Euclidean      25 383
Norm, matrix      26
Numerically unstable recursion      213
Nystrom method      180
Obrechkoff's method      77
ODE, linear      9
ODE, linear homogeneous      9
ODE, linear with constant coefficients      9
ODE, periodic      11
ODE, solution of      2
ODE, standard form of      2
Ohm's law      233
One-leg variant      220 229
One-step method      19 51
One-step-ahead prediction      164
Orbit      4 15
Orbital derivative      122
Order, of ODE      2
Orientation      304
Outer solution      207
Parameters      304
Parasitic root      177
Parasitic solutions      176
Parking      315
Partially separated BVP      277
Particle      280
Particular solution      86 87
PDE      296
PEC algorithm      186
PECE algorithm      187
Pendulum      248 287 311
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