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Numerical Continuation Methods

Tutor

Alexander Artiga Gonzalez

Schedule

Lecture Thu. 13:30 - 15:00 Z 613
 
Lab Session

Mo.

11:45 - 13:15

Z 613
       
Exam 1 Thu. 18.02.2016, 13:30 Z 613
Exam 2 Thu. 07.04.2016, 13:30 Z 613

Lab Sessions

The implementations can be made in MATLAB, C, C++ or another high-level language. We recommend Julia, which is a new high-performance dynamic programming language for technical computing that originates at the MIT and is rapidly extended by the open Julia developer community. Its syntax is familiar to users of other technical computing environments. It provides a sophisticated compiler, distributed parallel execution, numerical accuracy, and an extensive mathematical function library. The library, largely written in Julia itself, also integrates mature, best-of-breed C and Fortran libraries for linear algebra, random number generation, signal processing, and string processing.

Course works and credits

The course ends with a final exam (either oral or written, depending on the number of course participants). 50 % of the marks for homework assignments is required for the admission to this final exam.

Lab Sheets

  Date Due
Lab Sheet 1 22.10.2015 29.10.2015
Lab Sheet 202.11.201512.11.2015
Lab Sheet 324.11.201529.11.2015
Lab Sheet 406.12.201513.12.2015
Lab Sheet 514.12.201520.12.2015
Lab Sheet 611.01.201617.01.2016
Lab Sheet 724.01.201631.01.2016
Lab Sheet 804.02.201610.02.2016

Please submit your solutions as Latex-generated PDFs per e-mail to alexander.artiga-gonzalez@uni-konstanz.de.

 

 

Target Audience

Target Audience The course belongs to the topic areas Scientific Computing and Applied Computer Science and is for students of the following degree programs

  • Information Engineering und Computer Science, both for Bachelor Advanced Studies and Master
  • Mathematics
  • Physics

Prerequisites

Familiarity with analysis and linear algebra are required as well as programming skills.

Literature

Allgower, Eugene L., and Kurt Georg. Introduction to numerical continuation methods. Vol. 45. SIAM, 2003.

Gomes, Abel, et al. Implicit Curves and Surfaces: Mathematics, Data Structures and Algorithms: Mathematics, Data Structures and Algorithms. Springer Science & Business Media, 2009.

Seydel, Rüdiger. Practical bifurcation and stability analysis. Vol. 5. Springer Science & Business Media, 2009.

Seydel, Rüdiger. From equilibrium to chaos. Elsevier, 1988.

Weblinks

AUTO software for continuation and bifurcation problems in ordinary differential equations http://indy.cs.concordia.ca/auto/

R. Seydel (Ed.): World of Bifurcation. Online Collection and Tutorials of Nonlinear Phenomena http://www.bifurcation.de/index.html

Julia programming language home page

Julia Studio

Juno

Debug

Ipython / IJulia / Jupyter

Runge–Kutta–Verfahren