Introduction. Initial value problems, well-posedness, conditioning and regularity. One-step methods: consistency, stability, convergence, stiffness and integrals of motion. Multi-step methods.
Prerequisites for admission
Analysis and Linear Algebra. The basic knowledge of the programming language C.
Lectures, exercise and lab sessions.
P. Deuflhard, F. Bornemann, Scientific computing with ordinary differential equations, Springer 2002. E. Hairer, S. P. Norsett, G. Wanner, Solving ordinary differential equations I. Nonstiff problems, 2nd edition, Springer 1993. E. Hairer, G. Wanner, Solving ordinary differential equations II. Stiff and differential-algebraic problems, 2nd edition, Springer, 1996.
Assessment methods and Criteria
The final examination consists of two parts: - the correction of a report summarizing a small project to be chosen and - a final oral exam.
The project is chosen from a list that will be published at the end of the course, with specified validity. The project can be realized in collaboration with another person. The report summarizes the obtained results in at most 5 pages; it is recommended to write it not in collaboration. The correct submission of the project takes place at least two workdays before the oral exam and encompasses the report in pdf format, the used source codes (without executable files), and the name of the collaborator (if present).
The oral exam is on personal appointment after enrollment in an "appello". It starts with a discussion on the report. Subsequently, the student will be required to illustrate results presented during the course and will be required to solve problems in order to evaluate her/his knowledge and comprehension of the arguments covered as well as the capacity to apply them.
The complete examination is passed if the report and its discussion are evaluated positively and the oral exam is successfully passed. Final marks are given using the numerical range 0-30, and will be communicated immediately after the oral examination.