Methods and applications of singular perturbations: boundary layers and multiple timescale dynamics
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| Format: | Book |
| Language: | English |
| Published: |
New York
Springer
2005
|
| Series: | Texts in applied mathematics
50 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 324 S. graph. Darst. 25 cm |
| ISBN: | 0387229663 9780387229669 |
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MARC
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| 100 | 1 | |a Verhulst, Ferdinand |d 1939- |e Verfasser |0 (DE-588)111117755 |4 aut | |
| 245 | 1 | 0 | |a Methods and applications of singular perturbations |b boundary layers and multiple timescale dynamics |c Ferdinand Verhulst |
| 264 | 1 | |a New York |b Springer |c 2005 | |
| 300 | |a XV, 324 S. |b graph. Darst. |c 25 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Texts in applied mathematics |v 50 | |
| 650 | 4 | |a Perturbations singulières (Mathématiques) | |
| 650 | 4 | |a Problèmes aux limites - Solutions numériques | |
| 650 | 4 | |a Boundary value problems |x Numerical solutions | |
| 650 | 4 | |a Singular perturbations (Mathematics) | |
| 650 | 0 | 7 | |a Randwertproblem |0 (DE-588)4048395-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Singuläre Störung |0 (DE-588)4055100-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4123623-3 |a Lehrbuch |2 gnd-content | |
| 689 | 0 | 0 | |a Randwertproblem |0 (DE-588)4048395-2 |D s |
| 689 | 0 | 1 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |D s |
| 689 | 0 | 2 | |a Singuläre Störung |0 (DE-588)4055100-3 |D s |
| 689 | 0 | |5 DE-604 | |
| 830 | 0 | |a Texts in applied mathematics |v 50 |w (DE-604)BV002476038 |9 50 | |
| 856 | 4 | 2 | |m Digitalisierung UB Augsburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014183838&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-014183838 | ||
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| _version_ | 1804134582885285888 |
|---|---|
| adam_text | Contents
Preface
. . ......................................................
VII
1
Introduction
............................................... 1
2
Basic
Material
............................................. 9
2.1
Estimates and Order Symbols
............................. 9
2.2
Asymptotic Sequences and Series
.......................... 12
2.3
Asymptotic Expansions with more4 Variables
................ 13
2.4
Discussion
............................................... 16
2.4.1
The Question of Convergence
........................ 17
2.4.2
Practical Aspects of the
du
Bois-Reymond Theorem.
... 17
2.5
The Boundary of a Laser-Sustained Plasma
................. 18
2.
G
Guide to the Literature
.................................. 20
2.7
Exercises
............................................... 21
3
Approximation of Integrals
................................ 25
3.1
Partial Integration and the Laplace Integral
................. 25
3.2
Expansion of the Fourier Integral
.......................... 27
3.3
The Method of Stationary Phase
.......................... 27
3.4
Exercises
............................................... 28
4
Boundary Layer Behaviour
................................ 31
4.1
Regular Expansions and Boundary Layers
.................. 31
4.1.1
The Concept of a Boundary Layer
................... 33
4.2
A Ť
wo- Point Boundary Value Problem
..................... 35
4.3
Limits of Equations and Operators
........................ 38
4.4
Guide to the Literature
.................................. 41
4.5
Exercises
............................................... 42
XII
Contents
5
Two-Point Boundary Value Problems
...................... 43
õ.l
Boundary Layers at the Two
Endpoints.................... 43
•5.2
A Boundary Layer at One
Endpoint ....................... 48
5.3
The WKB.J Method
..................................... 52
5.4
A Curious Indeterminacy
................................. 54
5.5
Higher Order: The Suspension Bridge Problem
.............. 57
5.0
Guide to the Literature
.................................. 60
5.7
Exercises
...............................................
GO
6
Nonlinear Boundary Value Problems
...................... 63
6.1
Successful Use of Standard Techniques
..................... 64
6.1.1
The Equation
εφ
=
ô3............................
64
6.1.2
The Equation
εφ — φ2 ............................
65
6.1.3
A More General Equation
.......................... 66
6.2
An Intermezzo on Matching
.............................. 68
6.3
A Nonľmearity
with Unexpected Behaviour
................. 70
6.4
More Unexpected Behaviour. Spikes
....................... 72
6.4.1
Discussion
........................................ 74
6.5
Guide to the Literature
.................................. 74
6.6
Exercises
............................................... 75
7
Elliptic Boundary Value Problems
......................... 77
7.1
The Problem
εΔώ
-
φ =
ƒ
for
tlie
Circle
................... 77
7.2
The Problem
εΔψ
-щ=
f
for the Circle
.................. 80
7.3
The Problem
εΔό
-
§f
= ƒ
for the Rectangle
............... 84
7.4
Noncouvex Domains
..................................... 87
7.5
The Equation
εΔό
—
gj
= ƒ
on a Cube
.................... 89
7.6
Guide to the Literature
.................................. 89
7.7
Exercises
............................................... 90
8
Boundary Layers in Time
.................................. 93
8.1
Two Linear Second-Order Problems
......................... 94
8.2
Attraction of the Outer Expansion
......................... 99
8.3
The O Malley-Vasil eva Expansion
.........................102
8.4
The Two-Body Problem with Variable Mass
................105
8.5
The Slow Manifold:
Fenicheľs
Results
......................108
8.5.1
Existence of the Slow Manifold
......................109
8.5.2
The Compactness Property
.........................109
8.6
Behaviour near the Slow Manifold
.........................
Ill
8.6.
J
Approximating the Slow Manifold
...................
Ill
8.6.2
Extension of the Timescale
.........................112
8.7
Periodic Solutions and Oscillations
........................115
8.8
Guide to the Literature
..................................117
8.9
Exercises
...............................................119
Contents
XIII
9
Evolution Equations with Boundary Layers
................121
9.1
Slow Diffusion with Heat. Production
........................
L
21
9.1.1
The
Тії
ne-
Dependent Problem
......................122
9.2
Slow Diffusion on a Semi-infinite Domain
...................123
9.2.1
What Happens if p(t)
> 0? .........................125
9.3
A Chemical Reaction with Diffusion
.......................125
9.4
Periodic Solutions of Parabolic Equations
...................128
9.4.1
An Example
......................................128
9.4.2
The General
Caso
with Dirichlot. Conditions
..........130
9.4.3
Neumann Conditions
..............................131
9.4.4
Strongly Nonlinear Equations
.......................132
9.5
A Wave Equation
.......................................132
9.6
Signalling
..............................................136
9.7
Guide to the Literature
................................... 139
9.8
Exercises
...............................................140
10
The Continuation Method
.................................143
10.1
The
Poincaré
Expansion Theorem
.........................144
10.2
Periodic Solutions of Autonomous Equations
................146
] 0.3
Periodic Nonautonomous Equations
........................150
10.3.1
Frequency
ω
near
1................................155
10.3.2
Frequency
ω
near
2................................156
10.4
Autoparanietric Systems and Quenching
....................157
10.5
The Radius of Convergence
...............................160
10.
ö
Guide to the Literature
..................................161
10.7
Exercises
...............................................162
11
Averaging and Timescales
.................................165
11.1
Basic Periodic Averaging
..................................165
11.1.1
Transformation to a Slowly Varying System
...........169
11.1.2
The Asymptotic Character of Averaging
..............172
11.1.3
Quasiperiodic Averaging
...........................174
11.2
Nonperiodic Averaging
...................................175
11.3
Periodic Solutions
.......................................178
11.4
The Multiple-Timeseales Method
..........................181
11.5
Guide to the Literature
..................................184
11.6
Exercises
...............................................185
12
Advanced Averaging
.......................................187
12.1
Averaging over an Angle
.................................1.87
12.2
Averaging over more Angles
..............................192
12.2.1
General Formulation of Resonance
...................195
12.2.2
Nonautonomous Equations
.........................196
12.2.3
Passage through Resonance
.........................197
12.3
Invariant. Manifolds
......................................201
XIV
Contents
12.
3Л
Tori in
the
Dissipativi·
Case
........................202
12.3.2
The Neimark-Saeker Bifurcation
.....................206
12.3.3
Invariant Tori in the Hamiltonian Case
...............207
12.4
Adiabatie Invariants
.....................................210
12.5
Second-Order Periodic Averaging
..........................211
12.5.1
Procedure for Second-Order Calculation
..............212
12.5.2
An Unexpected Timeseale at Second-Order
...........215
12.6
Approximations Valid on Longer Timeseales
................
2JG
12.6.1
Approximations Valid on
O(l/f2)
...................217
12.6.2
Timeseales near Attracting Solutions
.................219
12.7
Identifying Timeseales
...................................221
12.7.1
Expected and Unexpected Timeseales
................221
12.7.2
Normal Forms. Averaging and Multiple Tiraescales
.... 222
12.8
Guide to the Literature
..................................223
12.9
Exercises
...............................................224
13
Averaging for Evolution Equations
........................ 227
13.1
Introduction
............................................227
13.2
Operators with a Continuous Spectrum
....................227
13.2.1
Averaging of Operators
............................228
13.2.2
Time-Periodic Advectioa-.Diflusion
...................229
13.3
Operators with a Discrete Spectrum
.......................230
КЗ. З.І
A General Averaging Theorem
......................231
13.3.2
Nonlinear Dispersive Waves
.........................232
13.3.3
Averaging and Truncation
......................... . 237
13.4
Guide to the Literature
...................................245
13.5
Exercises
...............................................246
14
Wave Equations on Unbounded Domains
..................249
14.1
The Linear Wave Equation with Dissipation
.................249
14.2
Averaging over the Characteristics
.........................251
14.3
A Weakly Nonlinear Klein-Gordon Equation
................254
14.4
Multiple Scaling and Variational Principles
.................256
14.5
Adiahatic Invariants and Energy Changes
..................260
14.6
The Perturbed Korteweg-de
Vries
Equation
.................
2G3
14.7
Guide to the Literature
..................................2(54
14.8
Exercises
...............................................265
15
Appendices
................................................267
15.1
The
du
Bois-Reymoud Theorem
...........................267
15.2
Approximation of Integrals
...............................268
15.3
Perturbations of Constant Matrices
........................269
15.3.1
General Results
...................................270
15.3.2
Some Examples
...................................273
15.4
Intermediate Matching
...................................276
(.
(»ut ont s
XV
15.5
Quadratic Boundary Value Problems
.......................279
10.5.1
No Roots
.........................................279
15.5.2
One Root
.........................................279
15.5.3
Two Roots
.......................................285
15.
ΰ
Application of Maximum Principles
........................288
15.7
Behaviour near the Slow Manifold
.........................290
15.7.1
The Proof by Jones and Kopell
(1994) ...............291
15.7.2
A Proof by Estimating Solutions
....................291
15.8
An Almost-Periodic Function
.............................293
15.9
Averaging for PDE s
.....................................295
15.9.1
A General Averaging Formulation
...................295
15.9.2
Averaging in
Danach
and Hubert Spaces
.............296
15.9.3
Application to Hyperbolic Equations
.................299
Epilogue
.......................................................301
Answers to Odd-Numbered Exercises
..........................303
Literature
.....................................................309
Index
..........................................................321
|
| adam_txt |
Contents
Preface
. . .
VII
1
Introduction
. 1
2
Basic
Material
. 9
2.1
Estimates and Order Symbols
. 9
2.2
Asymptotic Sequences and Series
. 12
2.3
Asymptotic Expansions with more4 Variables
. 13
2.4
Discussion
. 16
2.4.1
The Question of Convergence
. 17
2.4.2
Practical Aspects of the
du
Bois-Reymond Theorem.
. 17
2.5
The Boundary of a Laser-Sustained Plasma
. 18
2.
G
Guide to the Literature
. 20
2.7
Exercises
. 21
3
Approximation of Integrals
. 25
3.1
Partial Integration and the Laplace Integral
. 25
3.2
Expansion of the Fourier Integral
. 27
3.3
The Method of Stationary Phase
. 27
3.4
Exercises
. 28
4
Boundary Layer Behaviour
. 31
4.1
Regular Expansions and Boundary Layers
. 31
4.1.1
The Concept of a Boundary Layer
. 33
4.2
A Ť
wo- Point Boundary Value Problem
. 35
4.3
Limits of Equations and Operators
. 38
4.4
Guide to the Literature
. 41
4.5
Exercises
. 42
XII
Contents
5
Two-Point Boundary Value Problems
. 43
õ.l
Boundary Layers at the Two
Endpoints. 43
•5.2
A Boundary Layer at One
Endpoint . 48
5.3
The WKB.J Method
. 52
5.4
A Curious Indeterminacy
. 54
5.5
Higher Order: The Suspension Bridge Problem
. 57
5.0
Guide to the Literature
. 60
5.7
Exercises
.
GO
6
Nonlinear Boundary Value Problems
. 63
6.1
Successful Use of Standard Techniques
. 64
6.1.1
The Equation
εφ"
=
ô3.
64
6.1.2
The Equation
εφ" — φ2 .
65
6.1.3
A More General Equation
. 66
6.2
An Intermezzo on Matching
. 68
6.3
A Nonľmearity
with Unexpected Behaviour
. 70
6.4
More Unexpected Behaviour. Spikes
. 72
6.4.1
Discussion
. 74
6.5
Guide to the Literature
. 74
6.6
Exercises
. 75
7
Elliptic Boundary Value Problems
. 77
7.1
The Problem
εΔώ
-
φ =
ƒ
for
tlie
Circle
. 77
7.2
The Problem
εΔψ
-щ=
f
for the Circle
. 80
7.3
The Problem
εΔό
-
§f
= ƒ
for the Rectangle
. 84
7.4
Noncouvex Domains
. 87
7.5
The Equation
εΔό
—
gj
= ƒ
on a Cube
. 89
7.6
Guide to the Literature
. 89
7.7
Exercises
. 90
8
Boundary Layers in Time
. 93
8.1
Two Linear Second-Order Problems
. 94
8.2
Attraction of the Outer Expansion
. 99
8.3
The O'Malley-Vasil'eva Expansion
.102
8.4
The Two-Body Problem with Variable Mass
.105
8.5
The Slow Manifold:
Fenicheľs
Results
.108
8.5.1
Existence of the Slow Manifold
.109
8.5.2
The Compactness Property
.109
8.6
Behaviour near the Slow Manifold
.
Ill
8.6.
J
Approximating the Slow Manifold
.
Ill
8.6.2
Extension of the Timescale
.112
8.7
Periodic Solutions and Oscillations
.115
8.8
Guide to the Literature
.117
8.9
Exercises
.119
Contents
XIII
9
Evolution Equations with Boundary Layers
.121
9.1
Slow Diffusion with Heat. Production
.
L
21
9.1.1
The
Тії
ne-
Dependent Problem
.122
9.2
Slow Diffusion on a Semi-infinite Domain
.123
9.2.1
What Happens if p(t)
> 0? .125
9.3
A Chemical Reaction with Diffusion
.125
9.4
Periodic' Solutions of Parabolic Equations
.128
9.4.1
An Example
.128
9.4.2
The General
Caso
with Dirichlot. Conditions
.130
9.4.3
Neumann Conditions
.131
9.4.4
Strongly Nonlinear Equations
.132
9.5
A Wave Equation
.132
9.6
Signalling
.136
9.7
Guide to the Literature
. 139
9.8
Exercises
.140
10
The Continuation Method
.143
10.1
The
Poincaré
Expansion Theorem
.144
10.2
Periodic Solutions of Autonomous Equations
.146
] 0.3
Periodic Nonautonomous Equations
.150
10.3.1
Frequency
ω
near
1.155
10.3.2
Frequency
ω
near
2.156
10.4
Autoparanietric Systems and Quenching
.157
10.5
The Radius of Convergence
.160
10.
ö
Guide to the Literature
.161
10.7
Exercises
.162
11
Averaging and Timescales
.165
11.1
Basic Periodic Averaging
.165
11.1.1
Transformation to a Slowly Varying System
.169
11.1.2
The Asymptotic Character of Averaging
.172
11.1.3
Quasiperiodic Averaging
.174
11.2
Nonperiodic Averaging
.175
11.3
Periodic Solutions
.178
11.4
The Multiple-Timeseales Method
.181
11.5
Guide to the Literature
.184
11.6
Exercises
.185
12
Advanced Averaging
.187
12.1
Averaging over an Angle
.1.87
'12.2
Averaging over more Angles
.192
12.2.1
General Formulation of Resonance
.195
12.2.2
Nonautonomous Equations
.196
12.2.3
Passage through Resonance
.197
12.3
Invariant. Manifolds
.201
XIV
Contents
12.
3Л
Tori in
the
Dissipativi·
Case
.202
12.3.2
The Neimark-Saeker Bifurcation
.206
12.3.3
Invariant Tori in the Hamiltonian Case
.207
12.4
Adiabatie Invariants
.210
12.5
Second-Order Periodic Averaging
.211
12.5.1
Procedure for Second-Order Calculation
.212
12.5.2
An Unexpected Timeseale at Second-Order
.215
12.6
Approximations Valid on Longer Timeseales
.
2JG
12.6.1
Approximations Valid on
O(l/f2)
.217
12.6.2
Timeseales near Attracting Solutions
.219
12.7
Identifying Timeseales
.221
12.7.1
Expected and Unexpected Timeseales
.221
12.7.2
Normal Forms. Averaging and Multiple Tiraescales
. 222
12.8
Guide to the Literature
.223
12.9
Exercises
.224
13
Averaging for Evolution Equations
. 227
13.1
Introduction
.227
13.2
Operators with a Continuous Spectrum
.227
13.2.1
Averaging of Operators
.228
13.2.2
Time-Periodic Advectioa-.Diflusion
.229
13.3
Operators with a Discrete Spectrum
.230
КЗ.'З.І
A General Averaging Theorem
.231
13.3.2
Nonlinear Dispersive Waves
.232
13.3.3
Averaging and Truncation
. . 237
13.4
Guide to the Literature
.245
13.5
Exercises
.246
14
Wave Equations on Unbounded Domains
.249
14.1
The Linear Wave Equation with Dissipation
.249
14.2
Averaging over the Characteristics
.251
14.3
A Weakly Nonlinear Klein-Gordon Equation
.254
14.4
Multiple Scaling and Variational Principles
.256
14.5
Adiahatic Invariants and Energy Changes
.260
14.6
The Perturbed Korteweg-de
Vries
Equation
.
2G3
14.7
Guide to the Literature
.2(54
14.8
Exercises
.265
15
Appendices
.267
15.1
The
du
Bois-Reymoud Theorem
.267
15.2
Approximation of Integrals
.268
15.3
Perturbations of Constant Matrices
.269
15.3.1
General Results
.270
15.3.2
Some Examples
.273
15.4
Intermediate Matching
.276
(.
'(»ut ont s
XV
15.5
Quadratic Boundary Value Problems
.279
10.5.1
No Roots
.279
15.5.2
One Root
.279
15.5.3
Two Roots
.285
15.
ΰ
Application of Maximum Principles
.288
15.7
Behaviour near the Slow Manifold
.290
15.7.1
The Proof by Jones and Kopell
(1994) .291
15.7.2
A Proof by Estimating Solutions
.291
15.8
An Almost-Periodic Function
.293
15.9
Averaging for PDE's
.295
15.9.1
A General Averaging Formulation
.295
15.9.2
Averaging in
Danach
and Hubert Spaces
.296
15.9.3
Application to Hyperbolic Equations
.299
Epilogue
.301
Answers to Odd-Numbered Exercises
.303
Literature
.309
Index
.321 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Verhulst, Ferdinand 1939- |
| author_GND | (DE-588)111117755 |
| author_facet | Verhulst, Ferdinand 1939- |
| author_role | aut |
| author_sort | Verhulst, Ferdinand 1939- |
| author_variant | f v fv |
| building | Verbundindex |
| bvnumber | BV020862304 |
| callnumber-first | Q - Science |
| callnumber-label | QA379 |
| callnumber-raw | QA379 |
| callnumber-search | QA379 |
| callnumber-sort | QA 3379 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 500 SK 920 SK 520 SK 540 |
| classification_tum | MAT 418f |
| ctrlnum | (OCoLC)57475894 (DE-599)BVBBV020862304 |
| dewey-full | 515/.35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.35 |
| dewey-search | 515/.35 |
| dewey-sort | 3515 235 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV020862304 |
| illustrated | Illustrated |
| index_date | 2024-07-02T13:23:23Z |
| indexdate | 2024-07-09T20:26:54Z |
| institution | BVB |
| isbn | 0387229663 9780387229669 |
| language | English |
| lccn | 2005042479 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014183838 |
| oclc_num | 57475894 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-706 DE-20 DE-384 DE-83 DE-11 DE-188 |
| owner_facet | DE-91G DE-BY-TUM DE-706 DE-20 DE-384 DE-83 DE-11 DE-188 |
| physical | XV, 324 S. graph. Darst. 25 cm |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Springer |
| record_format | marc |
| series | Texts in applied mathematics |
| series2 | Texts in applied mathematics |
| spelling | Verhulst, Ferdinand 1939- Verfasser (DE-588)111117755 aut Methods and applications of singular perturbations boundary layers and multiple timescale dynamics Ferdinand Verhulst New York Springer 2005 XV, 324 S. graph. Darst. 25 cm txt rdacontent n rdamedia nc rdacarrier Texts in applied mathematics 50 Perturbations singulières (Mathématiques) Problèmes aux limites - Solutions numériques Boundary value problems Numerical solutions Singular perturbations (Mathematics) Randwertproblem (DE-588)4048395-2 gnd rswk-swf Singuläre Störung (DE-588)4055100-3 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Randwertproblem (DE-588)4048395-2 s Numerisches Verfahren (DE-588)4128130-5 s Singuläre Störung (DE-588)4055100-3 s DE-604 Texts in applied mathematics 50 (DE-604)BV002476038 50 Digitalisierung UB Augsburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014183838&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Verhulst, Ferdinand 1939- Methods and applications of singular perturbations boundary layers and multiple timescale dynamics Texts in applied mathematics Perturbations singulières (Mathématiques) Problèmes aux limites - Solutions numériques Boundary value problems Numerical solutions Singular perturbations (Mathematics) Randwertproblem (DE-588)4048395-2 gnd Singuläre Störung (DE-588)4055100-3 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4048395-2 (DE-588)4055100-3 (DE-588)4128130-5 (DE-588)4123623-3 |
| title | Methods and applications of singular perturbations boundary layers and multiple timescale dynamics |
| title_auth | Methods and applications of singular perturbations boundary layers and multiple timescale dynamics |
| title_exact_search | Methods and applications of singular perturbations boundary layers and multiple timescale dynamics |
| title_exact_search_txtP | Methods and applications of singular perturbations boundary layers and multiple timescale dynamics |
| title_full | Methods and applications of singular perturbations boundary layers and multiple timescale dynamics Ferdinand Verhulst |
| title_fullStr | Methods and applications of singular perturbations boundary layers and multiple timescale dynamics Ferdinand Verhulst |
| title_full_unstemmed | Methods and applications of singular perturbations boundary layers and multiple timescale dynamics Ferdinand Verhulst |
| title_short | Methods and applications of singular perturbations |
| title_sort | methods and applications of singular perturbations boundary layers and multiple timescale dynamics |
| title_sub | boundary layers and multiple timescale dynamics |
| topic | Perturbations singulières (Mathématiques) Problèmes aux limites - Solutions numériques Boundary value problems Numerical solutions Singular perturbations (Mathematics) Randwertproblem (DE-588)4048395-2 gnd Singuläre Störung (DE-588)4055100-3 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Perturbations singulières (Mathématiques) Problèmes aux limites - Solutions numériques Boundary value problems Numerical solutions Singular perturbations (Mathematics) Randwertproblem Singuläre Störung Numerisches Verfahren Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014183838&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002476038 |
| work_keys_str_mv | AT verhulstferdinand methodsandapplicationsofsingularperturbationsboundarylayersandmultipletimescaledynamics |