Numerik der Differentialgleichungen

What it is about

You will learn numerical methods for solving ordinary and simple partial differential equations. Topics include stiff and non-stiff initial value problems, fundamentals of boundary value problems, and methods such as finite differences, finite elements, and spectral methods (focus on 1D, elliptic problems partly in 2D). By the end you will be able to understand, assess and apply basic algorithms on the computer as well as estimate discretization errors.

What you will be able to do

• Understand and apply integration methods for initial value problems (stiff and non-stiff)
• Insight into boundary value problems and optimal control (introduction)
• Basic knowledge of finite differences, finite elements and spectral methods
• Assess efficiency and accuracy of numerical algorithms
• Apply techniques to describe and estimate discretization errors
• Develop algorithms and implement them on the computer

What the module consists of

• LectureConveying the content through lectures and examples; motivation for independent study
• TutorialPractical programming examples, problem sheets and solutions for deeper understanding; increasing independence
• Computer experiments/programmingPractice and implementation of the algorithms; practical application

Teaching method

• Lecture with programming examplesIntroduction to theory and examples; encouragement for independent engagement
• Tutorial with practical programming examplesDeepening through exercises, solutions and computer experiments
• Self-study with exercises and programming tasksReview and deepening of what is learned; increasing independence