FSF3566 Numerical Methods for ODEs and DAEs 7.5 credits

• 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.

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.

G. Dahlquist, Numerical Methods for Ordinary Differential Equations, lecture notes.

P. Deuflhard, F. Bornemann, Scientific Computing with Ordinary Differential Equations, Springer, 2002.

E. Hairer, S. P. Nørsett, G. Wanner, Solving Ordinary Differential Equations, Vol I, Springer, 1993.

E. Hairer, G. Wanner, Solving Ordinary Differential Equations, Vol II, Springer, 1996.

If the course is discontinued, students may request to be examined during the following two academic years.

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

A proposal for the final examination project will be provided. If the student has a proposal for his/her own project, it can be used after approval by the course leader. Additionally, four homework assigmnets must be submitted.

Four homework assignments and a project completed.

Anna Nissen

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.