Numerical Integration of Time Dependent Differential Equations

The first part of the course is devoted to general techniques for solving ordinary differential equations, like Runge-Kutta and linear multistep methods. Then modern numerical methods for special applications are discussed, for instance differential equations with conservation laws or other underlying geometric structures. The last part of the course will treat time integration of partial differential equations. Modern schemes based on splitting and exponentials will be presented and analyzed.

1. Knowledge. The first part of the course is devoted to general techniques for solving ordinary differential equations, like Runge-Kutta and linear multistep methods. Then modern numerical methods for special applications are discussed, for instance differential equations with conservation laws or other underlying geometric structures. The last part of the course will treat time integration of partial differential equations. Modern schemes based on splitting and exponentials will be presented and analyzed. 2. Skills. The students should handle the techniques related to numerical solution of ordinary and partial differential equations, in particular Runge-Kutta methods and multistep methods. They should be able to analyse modern methods for solving time dependent differential equations and use these methods in a variety of applied and theoretical problems. 3. Competence. The students will be able to participate in scientific discussions and conduct researches at high international level regarding the numerical solution of ordinary and time-dependent partial differential equations. They should be able to participate and contribute to joint projects on this area of research.

Lectures, alternatively guided self-study.

The course will be taught as needed. If there are few PhD students, the course is only given as a guided self-study.