Modul

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

After attending the course, students can explain the concept and the advantages of splitting methods. They know important examples of such methods and typical problem classes to which these methods can be applied. They can explain the relation between classical order and accuracy, and they know the (classical) order conditions of such methods. Students can reproduce and explain error estimates for splitting methods for linear and nonlinear evolution equations, and to explain the essential steps of the proof as well as the relevance of the made assumptions.

None

• Concept and advantages of splitting methods
• Splitting methods for ordinary differential equations
• Baker-Campbell-Hausdorff formula and order conditions
• Tools from operator theory
• Splitting methods for linear evolution equations (Schrödinger equation, parabolic problems)
• Splitting methods for nonlinear evolution equations (nonlinear Schrödinger equation, Gross-Pitaevskii equation, Korteweg-de Vries equation)

Familiarity with ordinary differential equations, Runge-Kutta methods (construction, order, stability) and Sobolev spaces (definition, basic properties, Sobolev embeddings) is strongly recommended.

Total workload: 180 hours

Attendance: 60 hours

• lectures, problem classes, and examination

Self-studies: 120 hours

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