Numerical solution of ordinary differential equations:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Hoboken, NJ
Wiley
2009
|
| Series: | Pure and applied mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 252 S. Diagramme |
| ISBN: | 047004294X 9780470042946 |
Staff View
MARC
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| 245 | 1 | 0 | |a Numerical solution of ordinary differential equations |c Kendall E. Atkinson ; Weimin Han ; David Stewart |
| 264 | 1 | |a Hoboken, NJ |b Wiley |c 2009 | |
| 300 | |a XII, 252 S. |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Pure and applied mathematics | |
| 650 | 4 | |a Differential equations |x Numerical solutions | |
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| 700 | 1 | |a Stewart, David |d 1961- |e Verfasser |0 (DE-588)138178011 |4 aut | |
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Record in the Search Index
| _version_ | 1804138887623213056 |
|---|---|
| adam_text | CONTENTS
Introduction
1
1
Theory of differential equations: An introduction
3
1.1
General solvability theory
7
1.2
Stability of the initial value problem
8
1.3
Direction fields
11
Problems
13
2
Euler s method
15
2.1
Definition of Euler s method
16
2.2
Error analysis of Euler s method
21
2.3
Asymptotic error analysis
26
2.3.
і
Richardson extrapolation
28
2.4
Numerical stability
29
2.4.1
Rounding error accumulation
30
Problems
32
ix
X
CONTENTS
3 Systems
of differential equations
37
3.1
Higher-order differential equations
39
3.2
Numerical methods for systems
42
Problems
46
4
The backward
Euler
method and the trapezoidal method
49
4.1
The backward
Euler
method
51
4.2
The trapezoidal method
56
Problems
62
5
Taylor and Runge-Kutta methods
67
5.1
Taylor methods
68
5.2
Runge-Kutta methods
70
5.2.1
A general framework for explicit Runge-Kutta methods
73
5.3
Convergence, stability, and asymptotic error
75
5.3.1
Error prediction and control
78
5.4
Runge-Kutta-Fehlberg methods
80
5.5
MATLAB
codes
82
5.6
Implicit Runge-Kutta methods
86
5.6.1
Two-point collocation methods
87
Problems
89
6
Multistep methods
95
6.1
Adams-Bashforth methods
96
6.2
Adams-Moulton methods
101
6.3
Computer codes
104
6.3.1
MATLAB
ODE codes
105
Problems
106
7
General error analysis for multistep methods
111
7.1
Truncation error
112
7.2
Convergence
1
1
5
7.3
A general error analysis
117
7.3.1
Stability theory
Ц8
7.3.2
Convergence theory
122
7.3.3
Relative stability and weak stability
122
Problems
123
CONTENTS
ХІ
8
Stiff differential equations
127
8.1
The method of lines for a parabolic equation
131
8.1.1
MATLAB
programs for the method of lines
135
8.2
Backward differentiation formulas
140
8.3
Stability regions for multistep methods
141
8.4
Additional sources of difficulty
143
8.4.1
А
-stability
and L-stability
143
8.4.2
Time-varying problems and stability
145
8.5
Solving the finite-difference method
145
8.6
Computer codes
146
Problems
147
9
Implicit RK methods for stiff differential equations
149
9.1
Families of implicit Runge-Kutta methods
149
9.2
Stability of Runge-Kutta methods
154
9.3
Order reduction
156
9.4
Runge-Kutta methods for stiff equations in practice
160
Problems
161
10
Differential algebraic equations
163
10.1
Initial conditions and drift
165
10.2
DAEs as stiff differential equations
168
10.3
Numerical issues: higher index problems
169
10.4
Backward differentiation methods for DAEs
173
10.4.1
Tndex
1
problems
173
1
0.4.2
Index
2
problems
174
10.5
Runge-Kutta methods for DAEs
175
10.5.1
Index
1
problems
176
10.5.2
Index
2
problems
179
10.6
Index three problems from mechanics
181
10.6.1
Runge-Kutta methods for mechanical index
3
systems
183
10.7
Higher index DAEs
184
Problems
185
11
Two-point boundary value problems
187
11.1
A finite-difference method
188
1
Î
. 1.1
Convergence
190
Xli
CONTENTS
11.1.2
A numerical example
190
11.1.3
Boundary conditions involving the derivative
194
11.2
Nonlinear two-point boundary value problems
195
11.2.1
Finite difference methods
197
11.2.2
Shooting methods
201
11.2.3
Collocation methods
204
11.2.4
Other methods and problems
206
Problems
206
12
Volterra integral equations
211
12.1
Solvability theory
212
12.1.1
Special equations
214
12.2
Numerical methods
215
12.2.1
The trapezoidal method
216
12.2.2
Error for the trapezoidal method
217
12.2.3
General schema for numerical methods
219
12.3
Numerical methods: Theory
223
12.3.1
Numerical stability
225
12.3.2
Practical numerical stability
227
Problems
231
Appendix A. Taylor s Theorem
235
Appendix B. Polynomial interpolation
241
References
245
Index
250
|
| any_adam_object | 1 |
| author | Atkinson, Kendall E. 1940- Han, Weimin 1963- Stewart, David 1961- |
| author_GND | (DE-588)12286977X (DE-588)121177971 (DE-588)138178011 |
| author_facet | Atkinson, Kendall E. 1940- Han, Weimin 1963- Stewart, David 1961- |
| author_role | aut aut aut |
| author_sort | Atkinson, Kendall E. 1940- |
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| building | Verbundindex |
| bvnumber | BV035440994 |
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| ctrlnum | (OCoLC)243960534 (DE-599)BVBBV035440994 |
| dewey-full | 518/.63 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 518 - Numerical analysis |
| dewey-raw | 518/.63 |
| dewey-search | 518/.63 |
| dewey-sort | 3518 263 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV035440994 |
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| indexdate | 2024-07-09T21:35:20Z |
| institution | BVB |
| isbn | 047004294X 9780470042946 |
| language | English |
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| physical | XII, 252 S. Diagramme |
| publishDate | 2009 |
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| publisher | Wiley |
| record_format | marc |
| series2 | Pure and applied mathematics |
| spelling | Atkinson, Kendall E. 1940- Verfasser (DE-588)12286977X aut Numerical solution of ordinary differential equations Kendall E. Atkinson ; Weimin Han ; David Stewart Hoboken, NJ Wiley 2009 XII, 252 S. Diagramme txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics Differential equations Numerical solutions Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 s Numerische Mathematik (DE-588)4042805-9 s DE-604 Han, Weimin 1963- Verfasser (DE-588)121177971 aut Stewart, David 1961- Verfasser (DE-588)138178011 aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017361252&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Atkinson, Kendall E. 1940- Han, Weimin 1963- Stewart, David 1961- Numerical solution of ordinary differential equations Differential equations Numerical solutions Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Numerische Mathematik (DE-588)4042805-9 gnd |
| subject_GND | (DE-588)4020929-5 (DE-588)4042805-9 |
| title | Numerical solution of ordinary differential equations |
| title_auth | Numerical solution of ordinary differential equations |
| title_exact_search | Numerical solution of ordinary differential equations |
| title_full | Numerical solution of ordinary differential equations Kendall E. Atkinson ; Weimin Han ; David Stewart |
| title_fullStr | Numerical solution of ordinary differential equations Kendall E. Atkinson ; Weimin Han ; David Stewart |
| title_full_unstemmed | Numerical solution of ordinary differential equations Kendall E. Atkinson ; Weimin Han ; David Stewart |
| title_short | Numerical solution of ordinary differential equations |
| title_sort | numerical solution of ordinary differential equations |
| topic | Differential equations Numerical solutions Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Numerische Mathematik (DE-588)4042805-9 gnd |
| topic_facet | Differential equations Numerical solutions Gewöhnliche Differentialgleichung Numerische Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017361252&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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