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Recipes for Continuation

Recipes for Continuation


Part of Computational Science and Engineering

  • Date Published: August 2013
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial null Mathematics for availability.
  • format: Paperback
  • isbn: 9781611972566


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About the Authors
  • This 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
    Read more

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    Product details

    • Date Published: August 2013
    • format: Paperback
    • isbn: 9781611972566
    • length: 600 pages
    • dimensions: 254 x 177 x 29 mm
    • weight: 1.05kg
    • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial null Mathematics for availability.
  • 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

  • Authors

    Harry Dankowicz, University of Illinois, Urbana-Champaign
    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, Technical University of Denmark, Lyngby
    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.

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