Differential equations with small parameters and relaxation oscillations:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York
Plenum Pr.
1980
|
| Schriftenreihe: | Mathematical concepts and methods in science and engineering.
13. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | EST: Differencial'nye uravnenija s malym parametrom i relaksacionnye kolebanija (engl.) |
| Beschreibung: | X, 228 S. graph. Darst. |
| ISBN: | 0306392534 |
Internformat
MARC
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| 007 | t | ||
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| 100 | 1 | |a Miščenko, Evgenij F. |d 1922- |e Verfasser |0 (DE-588)129584665 |4 aut | |
| 240 | 1 | 0 | |a Differencial'nye uravnenija s malym parametrom i relaksacionnye kolebanija |
| 245 | 1 | 0 | |a Differential equations with small parameters and relaxation oscillations |c Evgenij F. Miščenko ; Nikolaj C. Rozov* |
| 264 | 1 | |a New York |b Plenum Pr. |c 1980 | |
| 300 | |a X, 228 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematical concepts and methods in science and engineering. |v 13. | |
| 500 | |a EST: Differencial'nye uravnenija s malym parametrom i relaksacionnye kolebanija (engl.) | ||
| 650 | 4 | |a Relaxation, Méthodes de (Mathématiques) | |
| 650 | 4 | |a Équations différentielles - Solutions numériques | |
| 650 | 4 | |a Équations différentielles - Théorie asymptotique | |
| 650 | 4 | |a Differential equations |x Asymptotic theory | |
| 650 | 4 | |a Differential equations |x Numerical solutions | |
| 650 | 4 | |a Relaxation methods (Mathematics) | |
| 650 | 0 | 7 | |a Gewöhnliche Differentialgleichung |0 (DE-588)4020929-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Asymptotik |0 (DE-588)4126634-1 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Asymptotik |0 (DE-588)4126634-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Gewöhnliche Differentialgleichung |0 (DE-588)4020929-5 |D s |
| 689 | 1 | 1 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |D s |
| 689 | 1 | |5 DE-604 | |
| 700 | 1 | |a Rozov, Nikolaj Ch. |e Verfasser |4 aut | |
| 830 | 0 | |a Mathematical concepts and methods in science and engineering. |v 13. |w (DE-604)BV000001144 |9 13. | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-001488930 | ||
Datensatz im Suchindex
| _version_ | 1804116723492716544 |
|---|---|
| adam_text | CONTENTS
Chapter I. Dependence of Solutions on Small Parameters.
Applications of Relaxation Oscillations
1. Smooth Dependence. Poincare s Theorem 1
2. Dependence of Solutions on a Parameter,
on an Infinite Time Interval 3
3. Equations with Small Parameters
Multiplying Derivatives 4
4. Second Order Systems. Fast and Slow Motion.
Relaxation Oscillations 9
5. Systems of Arbitrary Order. Fast and Slow
Motion. Relaxation Oscillations 16
6. Solutions of the Degenerate Equation
System 24
7. Asymptotic Expansions of Solutions with
Respect to a Parameter 29
8. A Sketch of the Principal Results 34
Chapter II. Second Order Systems. Asymptotic Calculation
of Solutions
1. Assumptions and Definitions 39
2. The Zeroth Approximation 45
vii
viii CONTENTS
3. Asymptotic Approximations on Slow Motion
Parts of the Trajectory 48
4. Proof of the Asymptotic Representations
of the Slow Motion Part 52
5. Local Coordinates in the Neighborhood
of a Junction Point 56
6. Asymptotic Approximations of the
Trajectory on the Initial Part of
a Junction 60
7. The Relation between Asymptotic Represen¬
tations and Actual Trajectories in
the Initial Junction Section 62
8. Special Variables for the Junction Section .... 67
9. A Riccati Equation 68
10. Asymptotic Approximations for the Trajectory
in the Neighborhood of a Junction
Point 72
11. The Relation between Asymptotic Approxima¬
tions and Actual Trajectories in the
Immediate Vicinity of a Junction
Point 77
12. Asymptotic Series for the Coefficients
of the Expansion Near a Junction
Point 82
13. Regularization of Improper Integrals 89
14. Asymptotic Expansions for the End of a
Junction Part of a Trajectory 96
15. The Relation between Asymptotic Approxi¬
mations and Actual Trajectories
at the End of a Junction Part 99
16. Proof of Asymptotic Representations for
the Junction Part 103
CONTENTS ix
17. Asymptotic Approximations of the
Trajectory on the Fast Motion
Part 107
18. Derivation of Asymptotic Representa¬
tions for the Fast Motion Part 111
19. Special Variables for the Drop Part 114
20. Asymptotic Approximations of the Drop
Part of the Trajectory 119
21. Proof of Asymptotic Representations for the
Drop Part of the Trajectory 125
22. Asymptotic Approximations of the Trajectory
for Initial Slow Motion and Drop
Parts 132
Chapter III. Second Order Systems. Almost Discontinuous
Periodic solutions
1. Existence and Uniqueness of an Almost
Discontinuous Periodic Solution 139
2. Asymptotic Approximations for the
Trajectory of a Periodic Solution 143
3. Calculation of the Slow Motion Time 144
4. Calculation of the Junction Time 145
5. Calculation of the Fast Mot ion Time 156
6. Calculation of the Drop Time 157
7. An Asymptotic Formula for the Relaxation
Oscillation Period 164
8. Van der Pol s Equation. Dorodnitsyn s
Formula 168
x CONTENTS
Chapter IV. Systems of Arbitrary Order. Asymptotic
Calculation of Solutions
1. Basic Assumptions 171
2. The Zeroth Approximation 173
3. Local Coordinates in the Neighborhood
of a Junction Point 176
A. Asymptotic Approximations of a Trajectory
at the Beginning of a Junction
Section 179
5. Asymptotic Approximations for the
Trajectory in the Neighborhood
of a Junction Point 187
6. Asymptotic Approximation of a Trajectory
at the End of a Junction Section 193
7. The Displacement Vector 196
Chapter V. Systems of Arbitrary Order. Almost Discontinuous
Periodic Solutions
1. Auxiliary Results 199
2. The Existence of an Almost Discontinuous
Periodic Solution. Asymptotic
Calculation of the Trajectory 203
3. An Asymptotic Formula for the Period of
Relaxation Oscillations 209
References 217
Index 223
|
| any_adam_object | 1 |
| author | Miščenko, Evgenij F. 1922- Rozov, Nikolaj Ch |
| author_GND | (DE-588)129584665 |
| author_facet | Miščenko, Evgenij F. 1922- Rozov, Nikolaj Ch |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV002265799 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:43:02Z |
| institution | BVB |
| isbn | 0306392534 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001488930 |
| oclc_num | 3748401 |
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| physical | X, 228 S. graph. Darst. |
| publishDate | 1980 |
| publishDateSearch | 1980 |
| publishDateSort | 1980 |
| publisher | Plenum Pr. |
| record_format | marc |
| series | Mathematical concepts and methods in science and engineering. |
| series2 | Mathematical concepts and methods in science and engineering. |
| spelling | Miščenko, Evgenij F. 1922- Verfasser (DE-588)129584665 aut Differencial'nye uravnenija s malym parametrom i relaksacionnye kolebanija Differential equations with small parameters and relaxation oscillations Evgenij F. Miščenko ; Nikolaj C. Rozov* New York Plenum Pr. 1980 X, 228 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematical concepts and methods in science and engineering. 13. EST: Differencial'nye uravnenija s malym parametrom i relaksacionnye kolebanija (engl.) Relaxation, Méthodes de (Mathématiques) Équations différentielles - Solutions numériques Équations différentielles - Théorie asymptotique Differential equations Asymptotic theory Differential equations Numerical solutions Relaxation methods (Mathematics) Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Asymptotik (DE-588)4126634-1 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 s Asymptotik (DE-588)4126634-1 s DE-604 Numerisches Verfahren (DE-588)4128130-5 s Rozov, Nikolaj Ch. Verfasser aut Mathematical concepts and methods in science and engineering. 13. (DE-604)BV000001144 13. HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001488930&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Miščenko, Evgenij F. 1922- Rozov, Nikolaj Ch Differential equations with small parameters and relaxation oscillations Mathematical concepts and methods in science and engineering. Relaxation, Méthodes de (Mathématiques) Équations différentielles - Solutions numériques Équations différentielles - Théorie asymptotique Differential equations Asymptotic theory Differential equations Numerical solutions Relaxation methods (Mathematics) Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Asymptotik (DE-588)4126634-1 gnd |
| subject_GND | (DE-588)4020929-5 (DE-588)4128130-5 (DE-588)4126634-1 |
| title | Differential equations with small parameters and relaxation oscillations |
| title_alt | Differencial'nye uravnenija s malym parametrom i relaksacionnye kolebanija |
| title_auth | Differential equations with small parameters and relaxation oscillations |
| title_exact_search | Differential equations with small parameters and relaxation oscillations |
| title_full | Differential equations with small parameters and relaxation oscillations Evgenij F. Miščenko ; Nikolaj C. Rozov* |
| title_fullStr | Differential equations with small parameters and relaxation oscillations Evgenij F. Miščenko ; Nikolaj C. Rozov* |
| title_full_unstemmed | Differential equations with small parameters and relaxation oscillations Evgenij F. Miščenko ; Nikolaj C. Rozov* |
| title_short | Differential equations with small parameters and relaxation oscillations |
| title_sort | differential equations with small parameters and relaxation oscillations |
| topic | Relaxation, Méthodes de (Mathématiques) Équations différentielles - Solutions numériques Équations différentielles - Théorie asymptotique Differential equations Asymptotic theory Differential equations Numerical solutions Relaxation methods (Mathematics) Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Asymptotik (DE-588)4126634-1 gnd |
| topic_facet | Relaxation, Méthodes de (Mathématiques) Équations différentielles - Solutions numériques Équations différentielles - Théorie asymptotique Differential equations Asymptotic theory Differential equations Numerical solutions Relaxation methods (Mathematics) Gewöhnliche Differentialgleichung Numerisches Verfahren Asymptotik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001488930&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000001144 |
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