Solving ordinary differential equations: 1 Nonstiff problems
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| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Berlin u.a.
Springer
2008
|
| Ausgabe: | 2. rev. ed., corr. 3. printing |
| Schriftenreihe: | Springer series in computational mathematics
8 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | XV, 528 S. graph. Darst. |
| ISBN: | 9783540566700 9783642051630 |
Internformat
MARC
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| 020 | |a 9783540566700 |9 978-3-540-56670-0 | ||
| 020 | |a 9783642051630 |c softcover |9 978-3-642-05163-0 | ||
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| 035 | |a (DE-599)BVBBV035184044 | ||
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| 245 | 1 | 0 | |a Solving ordinary differential equations |n 1 |p Nonstiff problems |c E. Hairer ; S. P. Nørsett ; G. Wanner |
| 250 | |a 2. rev. ed., corr. 3. printing | ||
| 264 | 1 | |a Berlin u.a. |b Springer |c 2008 | |
| 300 | |a XV, 528 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Springer series in computational mathematics |v 8 | |
| 490 | 0 | |a Springer series in computational mathematics |v ... | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 4 | |a Differential equations |x Numerical solutions | |
| 700 | 1 | |a Hairer, Ernst |d 1949- |e Sonstige |0 (DE-588)139445188 |4 oth | |
| 700 | 1 | |a Nørsett, Syvert P. |d 1944-2024 |e Sonstige |0 (DE-588)13758718X |4 oth | |
| 700 | 1 | |a Wanner, Gerhard |d 1942- |e Sonstige |0 (DE-588)13944534X |4 oth | |
| 773 | 0 | 8 | |w (DE-604)BV000612774 |g 1 |
| 830 | 0 | |a Springer series in computational mathematics |v 8 |w (DE-604)BV000012004 |9 8 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016990755&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-016990755 | |
Datensatz im Suchindex
| _version_ | 1809404445966991360 |
|---|---|
| adam_text |
Contents
Chapter I. Classical Mathematical Theory
1.1 Terminology
. 2
1.2
The Oldest Differential Equations
. 4
Newton
. 4
Leibniz and the Bernoulli Brothers
. 6
Variational Calculus
. 7
Clairaut
. 9
Exercises
. 10
1.3
Elementary Integration Methods
. 12
First Order Equations
. 12
Second Order Equations
. 13
Exercises
. 14
1.4
Linear Differential Equations
. 16
Equations with Constant Coefficients
. 16
Variation of Constants
.
І8
Exercises
. 19
1.5
Equations with Weak Singularities
. 20
Linear Equations
. 20
Nonlinear Equations
. 23
Exercises
. 24
1.6
Systems of Equations
. 26
The Vibrating String and Propagation of Sound
. 26
Fourier
. 29
Lagrangian Mechanics
. 30
Hamiltonian Mechanics
. 32
Exercises
. 34
1.7
A General Existence Theorem
. 35
Convergence of Euler's Method
. 35
Existence Theorem of Peano
. 41
Exercises
. 43
1.8
Existence Theory using Iteration Methods and Taylor Series
44
Picard-Lindelöf
Iteration
. 45
Taylor Series
. 46
Recursive Computation of Taylor Coefficients
. 47
Exercises
. 49
X
Contents
1.9
Existence
Theory for
Systems
of
Equations
. 51
Vector Notation
. 52
Subordinate Matrix Norms
. 53
Exercises
. 55
1.10
Differential Inequalities
. 56
Introduction
. 56
The Fundamental Theorems
. 57
Estimates Using One-Sided Lipschitz Conditions
. 60
Exercises
. 62
I.I
1
Systems of Linear Differential Equations
. 64
Resolvent and Wronskian
. 65
Inhomogeneous Linear Equations
. 66
The Abel-Liouville-Jacobi-Ostrogradskii Identity
. 66
Exercises
. 67
1.12
Systems with Constant Coefficients
. 69
Linearization
. 69
Diagonalization
. 69
The
Schur
Decomposition
. 70
Numerical Computations
. 72
The Jordan Canonical Form
. 73
Geometric Representation
. 77
Exercises
. 78
1.13
Stability
. 80
Introduction
. 80
The Routh-Hurwitz Criterion
. 81
Computational Considerations
. 85
Liapunov Functions
. 86
Stability of Nonlinear Systems
. 87
Stability of Non-Autonomous Systems
. 88
Exercises
. 89
1.14
Derivatives with Respect to Parameters and Initial Values
. 92
The Derivative with Respect to a Parameter
. 93
Derivatives with Respect to Initial Values
. 95
The Nonlinear Variation-of-Constants Formula
. 96
Flows and Volume-Preserving Flows
. 97
Canonical Equations and Symplectic Mappings
. 100
Exercises
. 104
1.15
Boundary Value and Eigenvalue Problems
. 105
Boundary Value Problems
. 105
Sturm-Liouville Eigenvalue Problems
. 107
Exercises
. 110
1.16
Periodic Solutions, Limit Cycles, Strange Attractors
.
Ill
Van
der Poľs
Equation
.
Ill
Chemical Reactions
. 115
Limit Cycles in Higher Dimensions,
Hopf
Bifurcation
. 117
Strange Attractors
. 120
The
Ups
and Downs of the
Lorenz
Model
. 123
Feigenbaum
Cascades
. 124
Exercises
. 126
Contents
XI
Chapter
IL Runge-Kutta and Extrapolation
Methods
ИЛ
The First Runge-Kutta
Methods
. 132
General Formulation
of
Runge-Kutta
Methods
. 134
Discussion
of Methods of Order
4. 135
"Optimal" Formulas
. 139
Numerical Example
. 140
Exercises
. 141
11.2 Order Conditions for Runge-Kutta Methods
. 143
The Derivatives of the True Solution
. 145
Conditions for Order
3. 145
Trees and Elementary Differentials
. 145
The Taylor Expansion of the True Solution
. 148
Faà di
Bruno's Formula
. 149
The Derivatives of the Numerical Solution
. 151
The Order Conditions
. 153
Exercises
. 154
11.3 Error Estimation and Convergence for RK Methods
. 156
Rigorous Error Bounds
. 156
The Principal Error Term
. 158
Estimation of the Global Error
. 159
Exercises
. 163
П.4
Practical Error Estimation and Step Size Selection
. 164
Richardson Extrapolation
. 164
Embedded Runge-Kutta Formulas
. 165
Automatic Step Size Control
. 167
Starting Step Size
. 169
Numerical Experiments
. 170
Exercises
. 172
11.5 Explicit Runge-Kutta Methods of Higher Order
. 173
The Butcher Barriers
. 173
6-Stage, 5th Order Processes
. 175
Embedded Formulas of Order
5 . 176
Higher Order Processes
. 179
Embedded Formulas of High Order
. 180
An 8th Order Embedded Method
. 181
Exercises
. 185
11.6 Dense Output, Discontinuities, Derivatives
. 188
Dense Output
. 188
Continuous Dormand
&
Prince Pairs
. 191
Dense Output for DOP853
. 194
Event Location
. 195
Discontinuous Equations
. 196
Numerical Computation of Derivatives with Respect
to Initial Values and Parameters
. 200
Exercises
. 202
И.7
Implicit Runge-Kutta Methods
. 204
Existence of a Numerical Solution
. 206
The Methods of Kuntzmann and Butcher of Order 2s
. 208
IRK Methods Based on Lobatto Quadrature
. 210
XII Contents
Collocation
Methods
. 211
Exercises
. 214
II.8 Asymptotic Expansion of the Global Error
. 216
The Global Error
. 216
Variable
h
.
2l8
Negative
h
. 219
Properties of the Adjoint Method
. 220
Symmetric Methods
. 221
Exercises
. 223
П.9
Extrapolation Methods
. 224
Definition of the Method
. 224
The Aitken
-
Neville Algorithm
. 226
The Gragg or GBS Method
. 228
Asymptotic Expansion for Odd Indices
. 231
Existence of Explicit RK Methods of Arbitrary Order
. 232
Order and Step Size Control
. 233
Dense Output for the GBS Method
. 237
Control of the Interpolation Error
. 240
Exercises
. 241
11.10
Numerical Comparisons
. 244
Problems
. 244
Performance of the Codes
. 249
A "Stretched" Error Estimator for DOP853
. 254
Effect of Step-Number Sequence in ODEX
. 256
11.11
Parallel Methods
. 257
Parallel Runge-Kutta Methods
. 258
Parallel Iterated Runge-Kutta Methods
. 259
Extrapolation Methods
. 261
Increasing Reliability
. 261
Exercises
. 263
11.12
Composition of B-Series
. 264
Composition of Runge-Kutta Methods
. 264
B-Series
. 266
Order Conditions for Runge-Kutta Methods
. 269
Butcher's "Effective Order"
. 270
Exercises
. 272
11.13
Higher Derivative Methods
. . 274
Collocation Methods
. 275
Hermite-Obreschkoff Methods
. 277
Fehlberg
Methods
. 278
General Theory of Order Conditions
. 280
Exercises
. 281
11.14
Numerical Methods for Second Order Differential Equations
283
Nyström
Methods
. 284
The Derivatives of the Exact Solution
. 286
The Derivatives of the Numerical Solution
. 288
The Order Conditions
. 290
On the Construction of
Nyström
Methods
. 291
An Extrapolation Method for y"
—
f(x, y)
. 294
Problems for Numerical Comparisons
. 296
Contents XIII
Performance
of the Codes
. 298
Exercises
. 300
11.15
P-Series for Partitioned Differential Equations
. 302
Derivatives of the Exact Solution, P-Trees
. 303
P-Series
. 306
Order Conditions for Partitioned Runge-Kutta Methods
. 307
Further Applications of P-Series
. 308
Exercises
. 311
11.16
Symplectic Integration Methods
. 312
Symplectic Runge-Kutta Methods
. 315
An Example from Galactic Dynamics
. 319
Partitioned Runge-Kutta Methods
. 326
Symplectic
Nyström
Methods
. 330
Conservation of the Hamiltonian; Backward Analysis
. 333
Exercises
. 337
11.17
Delay Differential Equations
. 339
Existence
. 339
Constant Step Size Methods for Constant Delay
. 341
Variable Step Size Methods
. 342
Stability
. 343
An Example from Population Dynamics
. 345
Infectious Disease Modelling
. 347
An Example from Enzyme Kinetics
. 248
A Mathematical Model in Immunology
. 349
Integro-Differential Equations
. 351
Exercises
. 352
Chapter III. Multistep Methods
and General Linear Methods
HI.l Classical Linear Multistep Formulas
. 356
Explicit Adams Methods
. 357
Implicit Adams Methods
. 359
Numerical Experiment
. 361
Explicit
Nyström
Methods
. 362
Milne-Simpson Methods
. 363
Methods Based on Differentiation (BDF)
. 364
Exercises
. 366
Ш.2
Local Error and Order Conditions
. 368
Local Error of a Multistep Method
. 368
Order of a Multistep Method
. 370
Error Constant
. 372
Irreducible Methods
. 374
The Peano Kernel of a Multistep Method
. 375
Exercises
. 377
IIL3 Stability and the First Dahlquist Barrier
. 378
Stability of the BDF-Formulas
. 380
Highest Attainable Order of Stable Multistep Methods
. 383
Exercises
. 387
XIV Contents
Ш.4
Convergence
of
Multistep
Methods
. 391
Formulation as One-Step Method
. 393
Proof of Convergence
. 395
Exercises
. 3%
Ш.5
Variable Step Size Multistep Methods
. 397
Variable Step Size Adams Methods
. 397
Recurrence Relations for 5j(n),
Фј(п)
and
Фј(п)
. 399
Variable Step Size BDF
. 400
General Variable Step Size Methods and Their Orders
. 401
Stability
. 402
Convergence
. 407
Exercises
. 409
111.6
Nordsieck Methods
. 410
Equivalence with Multistep Methods
. 412
Implicit Adams Methods
. 417
BDF-Methods
. 419
Exercises
. 420
Ш.7
Implementation and Numerical Comparisons
. 421
Step Size and Order Selection
. 421
Some Available Codes
. 423
Numerical Comparisons
. 427
Ш.8
General Linear Methods
. 430
A General Integration Procedure
. 431
Stability and Order
. 436
Convergence
. 438
Order Conditions for General Linear Methods
. 441
Construction of General Linear Methods
. 443
Exercises
. 445
Ш.9
Asymptotic Expansion of the Global Error
. 448
An Instructive Example
. 448
Asymptotic Expansion for Strictly Stable Methods
(8.4). 450
Weakly Stable Methods
. 454
The Adjoint Method
. 457
Symmetric Methods
. 459
Exercises
. 460
ШЛО
Multistep Methods for Second Order Differential Equations
461
Explicit
Stornier
Methods
. 462
Implicit
Stornier
Methods
. 464
Numerical Example
. 465
General Formulation
. 467
Convergence
. 468
Asymptotic Formula for the Global Error
. 471
Rounding Errors
. 472
Exercises
. 473
Appendix. Fortran Codes
. 475
Driver for the Code DOPRI5
. 475
Subroutine DOPRI5
. 477
Subroutine DOP853
. 481
Subroutine ODEX
. 482
Contents
XV
Subroutine 0DEX2
. 484
Driver for
the Code RETARD
. 486
Subroutine RETARD
. 488
Bibliography
. 491
Symbol Index
. 521
Subject Index
. 523 |
| adam_txt |
Contents
Chapter I. Classical Mathematical Theory
1.1 Terminology
. 2
1.2
The Oldest Differential Equations
. 4
Newton
. 4
Leibniz and the Bernoulli Brothers
. 6
Variational Calculus
. 7
Clairaut
. 9
Exercises
. 10
1.3
Elementary Integration Methods
. 12
First Order Equations
. 12
Second Order Equations
. 13
Exercises
. 14
1.4
Linear Differential Equations
. 16
Equations with Constant Coefficients
. 16
Variation of Constants
.
І8
Exercises
. 19
1.5
Equations with Weak Singularities
. 20
Linear Equations
. 20
Nonlinear Equations
. 23
Exercises
. 24
1.6
Systems of Equations
. 26
The Vibrating String and Propagation of Sound
. 26
Fourier
. 29
Lagrangian Mechanics
. 30
Hamiltonian Mechanics
. 32
Exercises
. 34
1.7
A General Existence Theorem
. 35
Convergence of Euler's Method
. 35
Existence Theorem of Peano
. 41
Exercises
. 43
1.8
Existence Theory using Iteration Methods and Taylor Series
44
Picard-Lindelöf
Iteration
. 45
Taylor Series
. 46
Recursive Computation of Taylor Coefficients
. 47
Exercises
. 49
X
Contents
1.9
Existence
Theory for
Systems
of
Equations
. 51
Vector Notation
. 52
Subordinate Matrix Norms
. 53
Exercises
. 55
1.10
Differential Inequalities
. 56
Introduction
. 56
The Fundamental Theorems
. 57
Estimates Using One-Sided Lipschitz Conditions
. 60
Exercises
. 62
I.I
1
Systems of Linear Differential Equations
. 64
Resolvent and Wronskian
. 65
Inhomogeneous Linear Equations
. 66
The Abel-Liouville-Jacobi-Ostrogradskii Identity
. 66
Exercises
. 67
1.12
Systems with Constant Coefficients
. 69
Linearization
. 69
Diagonalization
. 69
The
Schur
Decomposition
. 70
Numerical Computations
. 72
The Jordan Canonical Form
. 73
Geometric Representation
. 77
Exercises
. 78
1.13
Stability
. 80
Introduction
. 80
The Routh-Hurwitz Criterion
. 81
Computational Considerations
. 85
Liapunov Functions
. 86
Stability of Nonlinear Systems
. 87
Stability of Non-Autonomous Systems
. 88
Exercises
. 89
1.14
Derivatives with Respect to Parameters and Initial Values
. 92
The Derivative with Respect to a Parameter
. 93
Derivatives with Respect to Initial Values
. 95
The Nonlinear Variation-of-Constants Formula
. 96
Flows and Volume-Preserving Flows
. 97
Canonical Equations and Symplectic Mappings
. 100
Exercises
. 104
1.15
Boundary Value and Eigenvalue Problems
. 105
Boundary Value Problems
. 105
Sturm-Liouville Eigenvalue Problems
. 107
Exercises
. 110
1.16
Periodic Solutions, Limit Cycles, Strange Attractors
.
Ill
Van
der Poľs
Equation
.
Ill
Chemical Reactions
. 115
Limit Cycles in Higher Dimensions,
Hopf
Bifurcation
. 117
Strange Attractors
. 120
The
Ups
and Downs of the
Lorenz
Model
. 123
Feigenbaum
Cascades
. 124
Exercises
. 126
Contents
XI
Chapter
IL Runge-Kutta and Extrapolation
Methods
ИЛ
The First Runge-Kutta
Methods
. 132
General Formulation
of
Runge-Kutta
Methods
. 134
Discussion
of Methods of Order
4. 135
"Optimal" Formulas
. 139
Numerical Example
. 140
Exercises
. 141
11.2 Order Conditions for Runge-Kutta Methods
. 143
The Derivatives of the True Solution
. 145
Conditions for Order
3. 145
Trees and Elementary Differentials
. 145
The Taylor Expansion of the True Solution
. 148
Faà di
Bruno's Formula
. 149
The Derivatives of the Numerical Solution
. 151
The Order Conditions
. 153
Exercises
. 154
11.3 Error Estimation and Convergence for RK Methods
. 156
Rigorous Error Bounds
. 156
The Principal Error Term
. 158
Estimation of the Global Error
. 159
Exercises
. 163
П.4
Practical Error Estimation and Step Size Selection
. 164
Richardson Extrapolation
. 164
Embedded Runge-Kutta Formulas
. 165
Automatic Step Size Control
. 167
Starting Step Size
. 169
Numerical Experiments
. 170
Exercises
. 172
11.5 Explicit Runge-Kutta Methods of Higher Order
. 173
The Butcher Barriers
. 173
6-Stage, 5th Order Processes
. 175
Embedded Formulas of Order
5 . 176
Higher Order Processes
. 179
Embedded Formulas of High Order
. 180
An 8th Order Embedded Method
. 181
Exercises
. 185
11.6 Dense Output, Discontinuities, Derivatives
. 188
Dense Output
. 188
Continuous Dormand
&
Prince Pairs
. 191
Dense Output for DOP853
. 194
Event Location
. 195
Discontinuous Equations
. 196
Numerical Computation of Derivatives with Respect
to Initial Values and Parameters
. 200
Exercises
. 202
И.7
Implicit Runge-Kutta Methods
. 204
Existence of a Numerical Solution
. 206
The Methods of Kuntzmann and Butcher of Order 2s
. 208
IRK Methods Based on Lobatto Quadrature
. 210
XII Contents
Collocation
Methods
. 211
Exercises
. 214
II.8 Asymptotic Expansion of the Global Error
. 216
The Global Error
. 216
Variable
h
.
2l8
Negative
h
. 219
Properties of the Adjoint Method
. 220
Symmetric Methods
. 221
Exercises
. 223
П.9
Extrapolation Methods
. 224
Definition of the Method
. 224
The Aitken
-
Neville Algorithm
. 226
The Gragg or GBS Method
. 228
Asymptotic Expansion for Odd Indices
. 231
Existence of Explicit RK Methods of Arbitrary Order
. 232
Order and Step Size Control
. 233
Dense Output for the GBS Method
. 237
Control of the Interpolation Error
. 240
Exercises
. 241
11.10
Numerical Comparisons
. 244
Problems
. 244
Performance of the Codes
. 249
A "Stretched" Error Estimator for DOP853
. 254
Effect of Step-Number Sequence in ODEX
. 256
11.11
Parallel Methods
. 257
Parallel Runge-Kutta Methods
. 258
Parallel Iterated Runge-Kutta Methods
. 259
Extrapolation Methods
. 261
Increasing Reliability
. 261
Exercises
. 263
11.12
Composition of B-Series
. 264
Composition of Runge-Kutta Methods
. 264
B-Series
. 266
Order Conditions for Runge-Kutta Methods
. 269
Butcher's "Effective Order"
. 270
Exercises
. 272
11.13
Higher Derivative Methods
. . 274
Collocation Methods
. 275
Hermite-Obreschkoff Methods
. 277
Fehlberg
Methods
. 278
General Theory of Order Conditions
. 280
Exercises
. 281
11.14
Numerical Methods for Second Order Differential Equations
283
Nyström
Methods
. 284
The Derivatives of the Exact Solution
. 286
The Derivatives of the Numerical Solution
. 288
The Order Conditions
. 290
On the Construction of
Nyström
Methods
. 291
An Extrapolation Method for y"
—
f(x, y)
. 294
Problems for Numerical Comparisons
. 296
Contents XIII
Performance
of the Codes
. 298
Exercises
. 300
11.15
P-Series for Partitioned Differential Equations
. 302
Derivatives of the Exact Solution, P-Trees
. 303
P-Series
. 306
Order Conditions for Partitioned Runge-Kutta Methods
. 307
Further Applications of P-Series
. 308
Exercises
. 311
11.16
Symplectic Integration Methods
. 312
Symplectic Runge-Kutta Methods
. 315
An Example from Galactic Dynamics
. 319
Partitioned Runge-Kutta Methods
. 326
Symplectic
Nyström
Methods
. 330
Conservation of the Hamiltonian; Backward Analysis
. 333
Exercises
. 337
11.17
Delay Differential Equations
. 339
Existence
. 339
Constant Step Size Methods for Constant Delay
. 341
Variable Step Size Methods
. 342
Stability
. 343
An Example from Population Dynamics
. 345
Infectious Disease Modelling
. 347
An Example from Enzyme Kinetics
. 248
A Mathematical Model in Immunology
. 349
Integro-Differential Equations
. 351
Exercises
. 352
Chapter III. Multistep Methods
and General Linear Methods
HI.l Classical Linear Multistep Formulas
. 356
Explicit Adams Methods
. 357
Implicit Adams Methods
. 359
Numerical Experiment
. 361
Explicit
Nyström
Methods
. 362
Milne-Simpson Methods
. 363
Methods Based on Differentiation (BDF)
. 364
Exercises
. 366
Ш.2
Local Error and Order Conditions
. 368
Local Error of a Multistep Method
. 368
Order of a Multistep Method
. 370
Error Constant
. 372
Irreducible Methods
. 374
The Peano Kernel of a Multistep Method
. 375
Exercises
. 377
IIL3 Stability and the First Dahlquist Barrier
. 378
Stability of the BDF-Formulas
. 380
Highest Attainable Order of Stable Multistep Methods
. 383
Exercises
. 387
XIV Contents
Ш.4
Convergence
of
Multistep
Methods
. 391
Formulation as One-Step Method
. 393
Proof of Convergence
. 395
Exercises
. 3%
Ш.5
Variable Step Size Multistep Methods
. 397
Variable Step Size Adams Methods
. 397
Recurrence Relations for 5j(n),
Фј(п)
and
Фј(п)
. 399
Variable Step Size BDF
. 400
General Variable Step Size Methods and Their Orders
. 401
Stability
. 402
Convergence
. 407
Exercises
. 409
111.6
Nordsieck Methods
. 410
Equivalence with Multistep Methods
. 412
Implicit Adams Methods
. 417
BDF-Methods
. 419
Exercises
. 420
Ш.7
Implementation and Numerical Comparisons
. 421
Step Size and Order Selection
. 421
Some Available Codes
. 423
Numerical Comparisons
. 427
Ш.8
General Linear Methods
. 430
A General Integration Procedure
. 431
Stability and Order
. 436
Convergence
. 438
Order Conditions for General Linear Methods
. 441
Construction of General Linear Methods
. 443
Exercises
. 445
Ш.9
Asymptotic Expansion of the Global Error
. 448
An Instructive Example
. 448
Asymptotic Expansion for Strictly Stable Methods
(8.4). 450
Weakly Stable Methods
. 454
The Adjoint Method
. 457
Symmetric Methods
. 459
Exercises
. 460
ШЛО
Multistep Methods for Second Order Differential Equations
461
Explicit
Stornier
Methods
. 462
Implicit
Stornier
Methods
. 464
Numerical Example
. 465
General Formulation
. 467
Convergence
. 468
Asymptotic Formula for the Global Error
. 471
Rounding Errors
. 472
Exercises
. 473
Appendix. Fortran Codes
. 475
Driver for the Code DOPRI5
. 475
Subroutine DOPRI5
. 477
Subroutine DOP853
. 481
Subroutine ODEX
. 482
Contents
XV
Subroutine 0DEX2
. 484
Driver for
the Code RETARD
. 486
Subroutine RETARD
. 488
Bibliography
. 491
Symbol Index
. 521
Subject Index
. 523 |
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| id | DE-604.BV035184044 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:59:02Z |
| indexdate | 2024-09-06T00:29:07Z |
| institution | BVB |
| isbn | 9783540566700 9783642051630 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016990755 |
| oclc_num | 232978521 |
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| physical | XV, 528 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| series | Springer series in computational mathematics |
| series2 | Springer series in computational mathematics |
| spelling | Solving ordinary differential equations 1 Nonstiff problems E. Hairer ; S. P. Nørsett ; G. Wanner 2. rev. ed., corr. 3. printing Berlin u.a. Springer 2008 XV, 528 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer series in computational mathematics 8 Springer series in computational mathematics ... Hier auch später erschienene, unveränderte Nachdrucke Differential equations Numerical solutions Hairer, Ernst 1949- Sonstige (DE-588)139445188 oth Nørsett, Syvert P. 1944-2024 Sonstige (DE-588)13758718X oth Wanner, Gerhard 1942- Sonstige (DE-588)13944534X oth (DE-604)BV000612774 1 Springer series in computational mathematics 8 (DE-604)BV000012004 8 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016990755&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Solving ordinary differential equations Springer series in computational mathematics Differential equations Numerical solutions |
| title | Solving ordinary differential equations |
| title_auth | Solving ordinary differential equations |
| title_exact_search | Solving ordinary differential equations |
| title_exact_search_txtP | Solving ordinary differential equations |
| title_full | Solving ordinary differential equations 1 Nonstiff problems E. Hairer ; S. P. Nørsett ; G. Wanner |
| title_fullStr | Solving ordinary differential equations 1 Nonstiff problems E. Hairer ; S. P. Nørsett ; G. Wanner |
| title_full_unstemmed | Solving ordinary differential equations 1 Nonstiff problems E. Hairer ; S. P. Nørsett ; G. Wanner |
| title_short | Solving ordinary differential equations |
| title_sort | solving ordinary differential equations nonstiff problems |
| topic | Differential equations Numerical solutions |
| topic_facet | Differential equations Numerical solutions |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016990755&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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