Recipes for Continuation
Recipes for Continuation
Frank Schilder, Technical University of Denmark, Lyngby
£74.99
GBPThis book provides a comprehensive introduction to the mathematical methodology of parameter continuation. It develops a systematic formalism for constructing and implementing abstract representations of continuation problems with equal emphasis on theoretical rigor, algorithm development and software engineering. The book demonstrates the use of fully developed toolbox templates for boundary-value problems to the analysis of periodic orbits, quasi-periodic invariant tori, and connecting orbits between equilibria and/or periodic orbits. The book contains extensive and fully-worked examples that illustrate the application of the MATLAB-based Computational Continuation Core (COCO) to cutting-edge research in applied dynamical systems. Many exercises and open-ended projects on both theoretical and algorithmic aspects of the material are provided, suitable for self-study and course assignments. It is intended for students and teachers of nonlinear dynamics and engineering at the advanced undergraduate or first-year graduate level, as well as practitioners engaged in modeling dynamical systems or software development.
- Puts equal emphasis on theoretical rigour, algorithm development and software engineering
- Demonstrates the use of fully developed toolbox templates for the analysis of dynamical systems
- Fully-worked examples illustrate the application of the MATLAB-based Computational Continuation Core (COCO) to cutting edge research problems
Product details
August 2013Paperback
9781611972566
600 pages
254 × 177 × 29 mm
1.05kg
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Table of Contents
- Part I. Design Fundamentals:
- 1. A continuation paradigm
- 2. Encapsulation
- 3. Construction
- 4. Toolbox development
- 5. Task embedding
- Part II. Toolbox Templates:
- 6. Discretization
- 7. The collocation continuation problem
- 8. Single-segment continuation problems
- 9. Multisegment continuation problems
- 10. The variational collocation problem
- Part III. Atlas Algorithms:
- 11. Covering manifolds
- 12. Single-dimensional atlas algorithms
- 13. Multidimensional manifolds
- 14. Computational domains
- Part IV. Event Handling:
- 15. Special points and events
- 16. Atlas events and toolbox integration
- 17. Event handlers and branch switching
- Part V. Adaptation:
- 18. Pointwise adaptation and comoving meshes
- 19. A spectral toolbox
- 20. Integrating adaptation in atlas algorithms
- Part VI. Epilogue:
- 21. Toolbox projects
- Index.
