Modul

The module will be completed by an oral exam (about 30 min).

The central topic of the lecture are numerical time-integrators for highly oscillatory ordinary and partial differential equations.

After participation, students

• know selected classes of ordinary and partial differential equations with oscillatory solutions and can explain the reason for the oscillatons.
• can explain why time-integration of such problems with traditional methods is usually inefficient.
• know different techniques which can be used to construct more efficient methods for selected problems.
• can explain error bounds for such integrators and know the ideas, techniques and assumptions used in the error analysis.

none

• Oscillatory ordinary and partial differential equations: examples and applications
• Construction of time integrators
• Oscillations and resonances
• Error analysis
• Space discretization by Fourier collocation methods

Participants are expected to be familiar with numerical methods for ordinary differential equations (e.g. Runge-Kutta methods) and with concepts required for their analysis (stability, order, local and global error, etc.).

Total workload: 240 hours

Attendance: 90 h

• lectures, problem classes and examination

Self studies: 150 h

• follow-up and deepening of the course content,
• work on problem sheets,
• literature study and internet research on the course content,
• preparation for the module examination