Numerical Analysis of Nonlinear Equations

Automne 2007
Concordia University
Enseignant: Sebius Doedel

Topics: An introduction to numerical algorithms for nonlinear equations, including discrete as well as continuous systems. The emphasis is on computer-aided numerical analysis, rather than numerical simulation. This course is suitable for scientists and engineers with a practical interest in nonlinear phenomena. Topics include computational aspects of: homotopy and continuation methods, fixed points and stationary solutions, asymptotic stability, bifurcations, periodic solutions, transition to chaos, travelling wave solutions, discretization techniques. A variety of applications will be considered. Projects may be done on selected applications. Numerical software packages will be available.

Prerequisites: The official prerequisite is COMP 5611, which is equivalent to the undergraduate course COMP361 on Numerical Methods. Some knowledge of differential equations (especially computational, at an elementary level) will also be helpful.

Lecture notes: Printed lecture notes will be provided.
Recommended reference books: For a comprehensive treatment of relevant theory and related material: Yu. A. Kuznetsov, Elements of Applied Bifurcation Theory, Springer Verlag, 1995, 1998, 2004.
A more elementary reference book:
R. Seydel, Practical Bifurcation and Stability Analysis, 2nd ed., Elsevier, 1995.