Numerical solution of ordinary differential equations: for classical, relativistic and nano systems
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Weinheim
Wiley-VCH-Verl.
2006
|
| Schriftenreihe: | Physics textbook
|
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | X, 204 S. graph. Darst. |
| ISBN: | 9783527406104 3527406107 |
Internformat
MARC
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| 245 | 1 | 0 | |a Numerical solution of ordinary differential equations |b for classical, relativistic and nano systems |c Donald Greenspan |
| 264 | 1 | |a Weinheim |b Wiley-VCH-Verl. |c 2006 | |
| 300 | |a X, 204 S. |b graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804135107657728000 |
|---|---|
| adam_text | Contents
Preface
¡X
1
Euler s
Method
1
1.1
Introduction I
1.2
Euler s Method
1
1.3
Convergence of Euler s Method*
5
1.4
Remarks
8
1.5
Exercises
9
2
Runge-Kutta Methods
11
2.1
Introduction
її
2.2
A Runge-Kutta Formula
11
2.3
Higher-Order Runge-Kutta Formulas
15
2.4
Kutta s Fourth-Order Formula
22
2.5
Kutta s Formulas for Systems of First-Order Equations
23
2.6
Kutta s Formulas for Second-Order Differential Equations
26
2.7
Application
-
The Nonlinear Pendulum
28
2.8
Application
-
Impulsive Forces
31
2.9
Exercises
34
3
The Method of Taylor Expansions
37
3.1
Introduction
37
3.2
First-Order Problems
37
3.3
Systems of First-Order Equations
4Ű
3.4
Second-Order Initial Value Problems
41
3.5
Application
-
The van
der Pol
Oscillator
43
3.6
Exercises
45
Vi|
Contents
4
Large Second-Order Systems with Application to
Nano
Systems
49
4.1
Introduction
49
4.2
The N-Body Problem
49
4.3
Classical Molecular Potentials
50
4.4
Molecular Mechanics
52
4.5
The Leap Frog Formulas
52
4.6
Equations of Motion for Argon Vapor
53
4.7
A Cavity Problem
54
4.8
Computational Considerations
56
4.9
Examples of Primary Vortex Generation
56
4.10
Examples of Turbulent Flow
59
4.11
Remark
61
4.12
Molecular Formulas for Air
62
4.13
A Cavity Problem
63
4.14
Initial Data
64
4.15
Examples of Primary Vortex Generation
65
4.16
Turbulent Flow
66
4.17
Colliding
Microdrops
of Water Vapor
70
4.18
Remarks
72
4.19
Exercises
74
5
Completely Conservative, Covariant Numerical Methodology
77
5.1
Introduction
77
5.2
Mathematical Considerations
77
5.3
Numerical Methodology
78
5.4
Conservation Laws
79
5.5
Covariance
82
5.6
Application
-
A Spinning Top on a Smooth Horizontal Plane
85
5.7
Application
-
Calogero
and
Toda Hamiltonian
Systems
103
5.8
Remarks
108
5.9
Exercises
109
6
Instability
111
6.1
Introduction
221
6.2
Instability Analysis 111
6.3
Numerical Solution of Mildly Nonlinear Autonomous Systems
722
6.4
Exercises
130
7
Numerical Solution of Tridiagonal Linear Algebraic Systems and Related
Nonlinear Systems
133
7.1
Introduction
133
7.2
Tridiagonal Systems
133
Contents
VII
7.3
The Direct Method
136
7.4
The Newton-Lieberstein Method
137
7.5
Exercises
140
8
Approximate Solution of Boundary Value Problems
143
8.1
Introduction
143
8.2
Approximate Differentiation
143
8.3
Numerical Solution of Boundary Value Problems Using Difference
Equations
144
8.4
Upwind Differencing
148
8.5
Mildly Nonlinear Boundary Value Problems
150
8.6
Theoretical
Support*
152
8.7
Application
-
Approximation of Airy Functions
155
8.8
Exercises
156
9
Special Relativists Motion
159
9.1
Introduction
159
9.2
Inerţial
Frames
160
9.3
The
Lorentz
Transformation
161
9.4
Rod Contraction and Time Dilation
161
9.5
Relativistic Particle Motion
163
9.6
Covariance
163
9.7
Particle Motion
165
9.8
Numerical Methodology
166
9.9
Relativistic Harmonic Oscillation
169
9.10
Computational Covariance
270
9.11
Remarks
174
9.12
Exercises
175
10
Special Topics
177
10.1
Introduction
277
10.2
Solving Boundary Value Problems by Initial Value Techniques
277
10.3
Solving Initial Value Problems by Boundary Value Techniques 27S
10.4
Predictor-Corrector Methods
179
10.5
Multistep Methods
180
10.6
Other Methods
180
10.7
Consistency*
181
10.8
Differential Eigenvalue Problems
182
10.9
Chaos*
184
10.10
Contact Mechanics
184
Vlil
I Contents
Appendix
I Basic Matrix Operations
187
Solutions to Selected Exercises
191
References
197
Index
203
|
| adam_txt |
Contents
Preface
¡X
1
Euler's
Method
1
1.1
Introduction I
1.2
Euler's Method
1
1.3
Convergence of Euler's Method*
5
1.4
Remarks
8
1.5
Exercises
9
2
Runge-Kutta Methods
11
2.1
Introduction
її
2.2
A Runge-Kutta Formula
11
2.3
Higher-Order Runge-Kutta Formulas
15
2.4
Kutta's Fourth-Order Formula
22
2.5
Kutta's Formulas for Systems of First-Order Equations
23
2.6
Kutta's Formulas for Second-Order Differential Equations
26
2.7
Application
-
The Nonlinear Pendulum
28
2.8
Application
-
Impulsive Forces
31
2.9
Exercises
34
3
The Method of Taylor Expansions
37
3.1
Introduction
37
3.2
First-Order Problems
37
3.3
Systems of First-Order Equations
4Ű
3.4
Second-Order Initial Value Problems
41
3.5
Application
-
The van
der Pol
Oscillator
43
3.6
Exercises
45
Vi|
Contents
4
Large Second-Order Systems with Application to
Nano
Systems
49
4.1
Introduction
49
4.2
The N-Body Problem
49
4.3
Classical Molecular Potentials
50
4.4
Molecular Mechanics
52
4.5
The Leap Frog Formulas
52
4.6
Equations of Motion for Argon Vapor
53
4.7
A Cavity Problem
54
4.8
Computational Considerations
56
4.9
Examples of Primary Vortex Generation
56
4.10
Examples of Turbulent Flow
59
4.11
Remark
61
4.12
Molecular Formulas for Air
62
4.13
A Cavity Problem
63
4.14
Initial Data
64
4.15
Examples of Primary Vortex Generation
65
4.16
Turbulent Flow
66
4.17
Colliding
Microdrops
of Water Vapor
70
4.18
Remarks
72
4.19
Exercises
74
5
Completely Conservative, Covariant Numerical Methodology
77
5.1
Introduction
77
5.2
Mathematical Considerations
77
5.3
Numerical Methodology
78
5.4
Conservation Laws
79
5.5
Covariance
82
5.6
Application
-
A Spinning Top on a Smooth Horizontal Plane
85
5.7
Application
-
Calogero
and
Toda Hamiltonian
Systems
103
5.8
Remarks
108
5.9
Exercises
109
6
Instability
111
6.1
Introduction
221
6.2
Instability Analysis 111
6.3
Numerical Solution of Mildly Nonlinear Autonomous Systems
722
6.4
Exercises
130
7
Numerical Solution of Tridiagonal Linear Algebraic Systems and Related
Nonlinear Systems
133
7.1
Introduction
133
7.2
Tridiagonal Systems
133
Contents
VII
7.3
The Direct Method
136
7.4
The Newton-Lieberstein Method
137
7.5
Exercises
140
8
Approximate Solution of Boundary Value Problems
143
8.1
Introduction
143
8.2
Approximate Differentiation
143
8.3
Numerical Solution of Boundary Value Problems Using Difference
Equations
144
8.4
Upwind Differencing
148
8.5
Mildly Nonlinear Boundary Value Problems
150
8.6
Theoretical
Support*
152
8.7
Application
-
Approximation of Airy Functions
155
8.8
Exercises
156
9
Special Relativists Motion
159
9.1
Introduction
159
9.2
Inerţial
Frames
160
9.3
The
Lorentz
Transformation
161
9.4
Rod Contraction and Time Dilation
161
9.5
Relativistic Particle Motion
163
9.6
Covariance
163
9.7
Particle Motion
165
9.8
Numerical Methodology
166
9.9
Relativistic Harmonic Oscillation
169
9.10
Computational Covariance
270
9.11
Remarks
174
9.12
Exercises
175
10
Special Topics
177
10.1
Introduction
277
10.2
Solving Boundary Value Problems by Initial Value Techniques
277
10.3
Solving Initial Value Problems by Boundary Value Techniques 27S
10.4
Predictor-Corrector Methods
179
10.5
Multistep Methods
180
10.6
Other Methods
180
10.7
Consistency*
181
10.8
Differential Eigenvalue Problems
182
10.9
Chaos*
184
10.10
Contact Mechanics
184
Vlil
I Contents
Appendix
I Basic Matrix Operations
187
Solutions to Selected Exercises
191
References
197
Index
203 |
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| indexdate | 2024-07-09T20:35:15Z |
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| spelling | Greenspan, Donald 1928- Verfasser (DE-588)130583073 aut Numerical solution of ordinary differential equations for classical, relativistic and nano systems Donald Greenspan Weinheim Wiley-VCH-Verl. 2006 X, 204 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Physics textbook Differential equations Numerical solutions Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Gewöhnliche Differentialgleichung (DE-588)4020929-5 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2665948&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014627012&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Greenspan, Donald 1928- Numerical solution of ordinary differential equations for classical, relativistic and nano systems Differential equations Numerical solutions Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4020929-5 (DE-588)4128130-5 (DE-588)4123623-3 |
| title | Numerical solution of ordinary differential equations for classical, relativistic and nano systems |
| title_auth | Numerical solution of ordinary differential equations for classical, relativistic and nano systems |
| title_exact_search | Numerical solution of ordinary differential equations for classical, relativistic and nano systems |
| title_exact_search_txtP | Numerical solution of ordinary differential equations for classical, relativistic and nano systems |
| title_full | Numerical solution of ordinary differential equations for classical, relativistic and nano systems Donald Greenspan |
| title_fullStr | Numerical solution of ordinary differential equations for classical, relativistic and nano systems Donald Greenspan |
| title_full_unstemmed | Numerical solution of ordinary differential equations for classical, relativistic and nano systems Donald Greenspan |
| title_short | Numerical solution of ordinary differential equations |
| title_sort | numerical solution of ordinary differential equations for classical relativistic and nano systems |
| title_sub | for classical, relativistic and nano systems |
| topic | Differential equations Numerical solutions Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Differential equations Numerical solutions Gewöhnliche Differentialgleichung Numerisches Verfahren Lehrbuch |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=2665948&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014627012&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT greenspandonald numericalsolutionofordinarydifferentialequationsforclassicalrelativisticandnanosystems |