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Recipes for Continuation [Pehme köide]

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  • Formaat: Paperback / softback, 599 pages, kõrgus x laius x paksus: 229x152x29 mm, kaal: 1085 g, illustrations
  • Sari: Computational Science & Engineering
  • Ilmumisaeg: 30-May-2013
  • Kirjastus: Society for Industrial & Applied Mathematics,U.S.
  • ISBN-10: 1611972566
  • ISBN-13: 9781611972566
Teised raamatud teemal:
Recipes for ContinuationSuurem pilt
  • Formaat: Paperback / softback, 599 pages, kõrgus x laius x paksus: 229x152x29 mm, kaal: 1085 g, illustrations
  • Sari: Computational Science & Engineering
  • Ilmumisaeg: 30-May-2013
  • Kirjastus: Society for Industrial & Applied Mathematics,U.S.
  • ISBN-10: 1611972566
  • ISBN-13: 9781611972566
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781611972566.html
Märksõnad:
This book provides a comprehensive introduction to the mathematical methodology of parameter continuation, the computational analysis of families of solutions to nonlinear mathematical equations. It develops a systematic formalism for constructing abstract representations of continuation problems and for implementing these in an existing computational platform.

Recipes for Continuation:

Lends equal importance to theoretical rigor, algorithm development, and software engineering. Demonstrates the use of fully developed toolbox templates for single- and multisegment boundary-value problems to the analysis of periodic orbits in smooth and hybrid dynamical systems, quasi-periodic invariant tori, and homoclinic and heteroclinic connecting orbits between equilibria and/or periodic orbits. Shows the use of vectorization for optimal computational efficiency, an object-oriented paradigm for the modular construction of continuation problems, and adaptive discretization algorithms for guaranteed bounds on estimated errors. Contains extensive and fully worked examples that illustrate the application of the MATLAB-based Computational Continuation Core (COCO) to problems from recent research literature that are relevant to dynamical system models from mechanics, electronics, biology, economics, and neuroscience.
Preface ix
I Design Fundamentals 1(118)
1 A Continuation Paradigm
3(16)
1.1 Problem formulation
3(1)
1.2 An analytical solution
3(6)
1.3 A numerical solution
9(5)
1.4 Conclusions
14(1)
Exercises
14(5)
2 Encapsulation
19(18)
2.1 Solution measures and constraints
20(3)
2.2 Continuation problems
23(5)
2.3 Algorithm development
28(3)
2.4 Conclusions
31(1)
Exercises
32(5)
3 Construction
37(32)
3.1 Problem decomposition
37(5)
3.2 Staged construction
42(3)
3.3 The core interface
45(18)
3.4 Conclusions
63(1)
Exercises
64(5)
4 Toolbox Development
69(26)
4.1 Toolbox constructors
70(11)
4.2 Embeddability
81(5)
4.3 Object-oriented design
86(5)
4.4 Conclusions
91(1)
Exercises
92(3)
5 Task Embedding
95(24)
5.1 Tree decompositions
95(3)
5.2 A composite toolbox
98(10)
5.3 Toolbox settings
108(6)
5.4 Conclusions
114(1)
Exercises
114(5)
II Toolbox Templates 119(176)
6 Discretization
121(26)
6.1 The collocation zero problem
122(2)
6.2 Vectorization
124(12)
6.3 A vectorized zero problem
136(4)
6.4 Conclusions
140(1)
Exercises
141(6)
7 The Collocation Continuation Problem
147(36)
7.1 Problem definition
147(3)
7.2 Encoding
150(7)
7.3 Examples
157(21)
7.4 Conclusions
178(1)
Exercises
179(4)
8 Single-Segment Continuation Problems
183(30)
8.1 Boundary-value problems
184(7)
8.2 Periodic orbits
191(9)
8.3 Alternative embeddings
200(6)
8.4 Conclusions
206(1)
Exercises
207(6)
9 Multisegment Continuation Problems
213(38)
9.1 Boundary-value problems
213(5)
9.2 Quasi-periodic invariant tori
218(8)
9.3 Multisegment periodic orbits
226(18)
9.4 Conclusions
244(1)
Exercises
245(6)
10 The Variational Collocation Problem
251(44)
10.1 The first variational equation
251(13)
10.2 A variational zero problem
264(21)
10.3 Candidate boundary conditions
285(2)
10.4 Conclusions
287(1)
Exercises
288(7)
III Atlas Algorithms 295(88)
11 Covering Manifolds
297(22)
11.1 Theory and terminology
297(10)
11.2 A finite-state machine
307(4)
11.3 An object-oriented implementation
311(4)
11.4 Conclusions
315(1)
Exercises
315(4)
12 Single-Dimensional Atlas Algorithms
319(24)
12.1 An advancing local cover
320(8)
12.2 Adaptation and accelerated convergence
328(4)
12.3 An expanding-boundary algorithm
332(7)
12.4 Conclusions
339(1)
Exercises
340(3)
13 Multidimensional Manifolds
343(24)
13.1 A point-cloud algorithm
343(5)
13.2 A chart network
348(6)
13.3 Henderson's algorithm
354(9)
13.4 Conclusions
363(1)
Exercises
364(3)
14 Computational Domains
367(16)
14.1 A 1-dimensional atlas algorithm
368(6)
14.2 A 2-dimensional atlas algorithm
374(4)
14.3 Manifolds of resonant periodic orbits
378(2)
14.4 Conclusions
380(2)
Exercises
382(1)
IV Event Handling 383(90)
15 Special Points and Events
385(26)
15.1 Theoretical framework
385(9)
15.2 A continuation paradigm
394(3)
15.3 The core interface
397(8)
15.4 Conclusions
405(1)
Exercises
405(6)
16 Atlas Events and Toolbox Integration
411(28)
16.1 Event detection in atlas algorithms
411(10)
16.2 A toolbox template
421(10)
16.3 An alternative constructor
431(2)
16.4 Conclusions
433(1)
Exercises
434(5)
17 Event Handlers and Branch Switching
439(34)
17.1 Toolbox event handlers
440(8)
17.2 Bifurcations of periodic orbits
448(10)
17.3 Branch switching
458(10)
17.4 Conclusions
468(1)
Exercises
468(5)
V Adaptation 473(98)
18 Pointwise Adaptation and Comoving Meshes
475(34)
18.1 A brute-force approach
476(10)
18.2 (Co)moving meshes
486(4)
18.3 A comoving-mesh algorithm
490(12)
18.4 Conclusions
502(2)
Exercises
504(5)
19 A Spectral Toolbox
509(24)
19.1 The spectral continuation problem
509(8)
19.2 Encoding
517(6)
19.3 Adaptivity
523(4)
19.4 Conclusions
527(1)
Exercises
528(5)
20 Integrating Adaptation in Atlas Algorithms
533(38)
20.1 Adaptive mesh refinements
533(11)
20.2 Boundary-value problems
544(13)
20.3 Numerical comparisons
557(9)
20.4 Conclusions
566(1)
Exercises
567(4)
VI Epilogue 571(10)
21 Toolbox Projects
573(8)
21.1 Calculus of variations
573(2)
21.2 Nonlinear boundary conditions
575(1)
21.3 Connecting orbits
576(1)
21.4 Conclusions
577(1)
Exercises
577(4)
Index 581
Harry Dankowicz is Professor of Mechanical Science and Engineering at the University of Illinois, Urbana-Champaign. He is the author of a research monograph on chaos in Hamiltonian systems and a textbook on multibody mechanics, and serves as an Associate Editor of the SIAM Journal on Applied Dynamical Systems. Frank Schilder has held postdoctoral research and teaching positions at the University of Bristol, the University of Surrey, and the Technical University of Denmark. In addition to COCO, he is the author of TORCONT and RAUTO and a co-author of SYMPERCO.