The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Chichester [u.a.]
Wiley
1987
|
| Schriftenreihe: | A Wiley-Interscience publication
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 512 S. graph. Darst. |
| ISBN: | 0471910465 |
Internformat
MARC
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| 100 | 1 | |a Butcher, John C. |d 1933- |e Verfasser |0 (DE-588)13615638X |4 aut | |
| 245 | 1 | 0 | |a The numerical analysis of ordinary differential equations |b Runge-Kutta and general linear methods |c J. C. Butcher |
| 264 | 1 | |a Chichester [u.a.] |b Wiley |c 1987 | |
| 300 | |a XV, 512 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a A Wiley-Interscience publication | |
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| 650 | 0 | 7 | |a Runge-Kutta-Verfahren |0 (DE-588)4203408-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Gewöhnliche Differentialgleichung |0 (DE-588)4020929-5 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804115059405750272 |
|---|---|
| adam_text | Contents
Chapter 1 Mathematical and computational introduction 1
10 Mathematical preliminaries 1
100 Vectors, matrices and norms
101 Multilinear functions
102 Calculus in vector spaces
103 Partial derivatives
104 The characteristic and minimal polynomials
105 Convergent and stable matrices
106 Metric spaces
107 Uniform boundedness and equicontinuity
11 Ordinary differential equations 16
110 Introduction to ordinary differential equations
111 Examples of differential equations
112 Fundamental theory of differential equations
113 Linear differential equations
114 Stability of differential equations
12 Difference equations 37
120 Introduction to difference equations
121 Linear difference equations with constant coefficients
122 Matrix difference equations
123 Stability of solutions to difference equations
13 Numerical approximation 47
130 Introduction to numerical approximation
131 The interpolational polynomial
132 Hermite interpolation
133 The calculus of finite differences
134 Numerical quadrature
135 Errors in numerical approximation
136 Rational interpolation
137 Pade approximations
14 Graphs and combinatorics 79
140 Graphs
xi
xii
141 A tree enumeration problem
142 Directed graphs
143 Notations for trees
144 Some functions defined on trees
145 Some enumeration problems
146 An algebraic structure related to trees
Chapter 2 The Euler method and its generalizations 105
20 The Euler method 105
200 Introduction
201 Local truncation error
202 Global truncation error
203 Convergence of the Euler method
204 Order of convergence
205 Asymptotic error formula
206 Stability characteristics
207 Rounding error
21 Generalizations of the Euler method 120
210 Introduction
211 More computations in a step
212 Dependence on more previous values
213 Use of higher derivatives
214 Multistep multistage multiderivative methods
215 Implicit methods
216 Local error estimates
217 Composite cyclic methods
218 Extrapolation methods
22 Runge Kutta methods 128
220 Historical introduction
221 General form of explicit Runge Kutta methods
222 Consistency and convergence
223 Order conditions
224 Examples of methods
225 Numerical examples
23 Linear multistep methods 135
230 Historical introduction
231 General form of linear multistep methods
232 Consistency, stability and convergence
233 Order conditions
234 Predictor corrector methods
235 Examples of methods
236 Numerical examples
24 Taylor series methods 146
240 Introduction to Taylor series methods
241 Manipulation of power series
242 An example of a Taylor series solution
243 Numerical results
244 Other methods using higher derivatives
245 The use of/derivatives
xiii
Chapter 3 Analysis of Runge Kutta methods 152
30 The order conditions 152
300 The order of two stage methods
301 Elementary differentials
302 The Taylor series for the differential equation solution
303 The Taylor series for the implicit Euler method
304 Elementary weights
305 The Taylor series for the Runge Kutta solution
306 Values of elementary weights and differentials
307 The order conditions
31 Low order explicit methods 173
310 Methods with orders less than four
311 The last stage of fourth order methods
312 Fourth order methods
313 The classical Runge—Kutta method
314 Gill s Runge Kutta method
32 The attainable order of explicit methods 184
320 Introductory comments
321 An elementary bound
322 Impossibility of five stage fifth order methods
323 Impossibility of p stage pth order methods with p 5
324 A sequence of bounds
325 A lower bound
326 Summary of known bounds
33 High order explicit methods 194
330 Row simplifying assumptions
331 Column simplifying assumptions
332 Fifth order methods
333 A generalization of fifth order methods
334 Sixth order methods
335 Methods of orders seven or more
34 Implicit Runge Kutta methods 209
340 Introduction
341 Implementation
342 The effect of simplifying assumptions
343 Methods based on Gauss Legendre quadrature
344 Reflected methods
345 Methods of order 2s , 2s 2
346 Collocation methods
347 Semi implicit methods
348 Singly implicit methods
35 Stability properties of Runge Kutta methods 237
350 Stability analysis
351 Stability regions for explicit methods
352 /4 stable methods
353 Further ^4 stable methods
354 Order stars and stability
355 ^N stability
356 Non linear stability
357 Generalizations of algebraic stability
xiv
358 The W transformation
359 Solvability of the algebraic equations
36 Error propagation in Runge Kutta methods 275
360 Introduction to error propagation
361 Local truncation error
362 The principal error function
363 Optimal methods
364 Global truncation error
365 Optimal order and stepsize sequences
366 S stability and stiff order
367 B consistency and S convergence
368 Runge Kutta methods with even error expansions
37 Runge Kutta methods with error estimates 294
370 Introduction
371 Richardson error estimates
372 Methods with built in estimates
373 A class of error estimating methods
374 The methods of E. Fehlberg
375 The methods of J. H. Verner
376 Further error estimating methods
377 Embedded implicit methods
38 Algebraic properties of Runge Kutta methods 311
380 The Runge Kutta space
381 Multiplication in the Runge Kutta space
382 Algebraic properties of the Runge Kutta space
383 Graph theoretic representation
384 The Runge Kutta homomorphism theorem
385 The image of the ideals Ip
386 The element E
387 The element D and the order of Runge Kutta methods
388 Miscellaneous constructs
389 Examples of Runge Kutta space usage
Chapter 4 General linear methods 335
40 Introduction to general linear methods 335
400 General classes of methods
401 Representation by matrices
402 Reduction to standard case
403 Generalizations
404 Implementation
41 Examples of general linear methods 340
410 Runge Kutta methods as examples
411 Linear multistep methods as examples
412 Predictor corrector methods as examples
413 Modified multistep methods as examples
414 One leg methods as examples
415 Miscellaneous examples
42 Stability, consistency and convergence 352
420 Stability
XV
421 Consistency
422 Convergence
423 Necessity of stability
424 Necessity of consistency
425 A lemma on stable sequences
426 Sufficiency of stability with consistency
427 Generalizations
43 Order of accuracy 370
430 Natural definitions of order
431 Order relative to a starting procedure
432 Algebraic criteria for order
433 Global error estimates
434 Particular cases
435 Effective order of Runge Kutta methods
44 Stability properties of general linear methods 388
440 Linear and non linear stability
441 Linear stability
442 Relationships between linear stability properties
443 Monotonic problems and methods
444 Algebraic stability for general linear methods
445 An example of an algebraically stable method
446 The equivalence of Euclidean AN and algebraic stabilities
447 Generalizations of algebraic stability
45 Practical prospects for general linear methods 400
450 Survey of possible methods
451 A fourth order Runge Kutta Nordsieck method
452 A fifth order Runge Kutta multistep method
453 General linear methods for stiff problems
Bibliography 408
Additional references 504
Index 506
|
| any_adam_object | 1 |
| author | Butcher, John C. 1933- |
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| author_facet | Butcher, John C. 1933- |
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| author_sort | Butcher, John C. 1933- |
| author_variant | j c b jc jcb |
| building | Verbundindex |
| bvnumber | BV000613165 |
| classification_rvk | SK 500 SK 920 |
| classification_tum | MAT 665f |
| ctrlnum | (OCoLC)241868492 (DE-599)BVBBV000613165 |
| dewey-full | 515'.352 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515'.352 |
| dewey-search | 515'.352 |
| dewey-sort | 3515 3352 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T15:16:35Z |
| institution | BVB |
| isbn | 0471910465 |
| language | English |
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| physical | XV, 512 S. graph. Darst. |
| publishDate | 1987 |
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| series2 | A Wiley-Interscience publication |
| spelling | Butcher, John C. 1933- Verfasser (DE-588)13615638X aut The numerical analysis of ordinary differential equations Runge-Kutta and general linear methods J. C. Butcher Chichester [u.a.] Wiley 1987 XV, 512 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier A Wiley-Interscience publication Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Runge-Kutta-Verfahren (DE-588)4203408-5 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Runge-Kutta-Verfahren (DE-588)4203408-5 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000381711&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Butcher, John C. 1933- The numerical analysis of ordinary differential equations Runge-Kutta and general linear methods Numerisches Verfahren (DE-588)4128130-5 gnd Runge-Kutta-Verfahren (DE-588)4203408-5 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| subject_GND | (DE-588)4128130-5 (DE-588)4203408-5 (DE-588)4020929-5 |
| title | The numerical analysis of ordinary differential equations Runge-Kutta and general linear methods |
| title_auth | The numerical analysis of ordinary differential equations Runge-Kutta and general linear methods |
| title_exact_search | The numerical analysis of ordinary differential equations Runge-Kutta and general linear methods |
| title_full | The numerical analysis of ordinary differential equations Runge-Kutta and general linear methods J. C. Butcher |
| title_fullStr | The numerical analysis of ordinary differential equations Runge-Kutta and general linear methods J. C. Butcher |
| title_full_unstemmed | The numerical analysis of ordinary differential equations Runge-Kutta and general linear methods J. C. Butcher |
| title_short | The numerical analysis of ordinary differential equations |
| title_sort | the numerical analysis of ordinary differential equations runge kutta and general linear methods |
| title_sub | Runge-Kutta and general linear methods |
| topic | Numerisches Verfahren (DE-588)4128130-5 gnd Runge-Kutta-Verfahren (DE-588)4203408-5 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| topic_facet | Numerisches Verfahren Runge-Kutta-Verfahren Gewöhnliche Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000381711&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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