Recipes for Continuation

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.

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.