FSF3566 Numerical Methods for ODEs and DAEs

This course is designed for PhD students in applied and computational mathematics, but it is suitable also for other PhD students with a background in computation with mathematical interests. The students are expected to have taken the basic and a continuation course in numerical analysis or acquired equivalent knowledge in a different way.

• One-step methods, convergence, stability, stiffness
• Errors, adaptivity
• Runge-Kutta methods, accuracy conditions, stability
• Preservation of invariants, symplectic methods
• Linear multistep methods, errors, stability, implementation issues
• Analytic properties of DAEs
• Numerical methods for DAEs and their properties

The course will give the students an introduction to the construction principles, theory, and implementation issues of modern methods for ODEs and DAEs.

After completion of the course the students can

• construct advanced numerical methods for ODEs and DAEs;
• investigate consistence and stability for given numerical methods;
• construct stepsize controllers and analyze their control theoretic properties;
• analyze the analytical properties of and DAEs;
• analyze the asymptotic properties of numerical integration schemes.