02685 Scientific Computing for Differential Equations

02685 Scientific Computing for Differential Equatons is given in the spring semester
every monday, 08:00-12:00, and every thursday, 13:00-17:00.

In that course, I give 6 lectures related to Runge-Kutta methods for systems of differential equations.

References and Books

• Michael T. Heath: Scientific Computing. An Introductory Survey. McGraw-Hill, 2005

• Timothy Sauer: Numerical Analysis. Pearson, 2nd Edition, 2014

• Uri M. Ascher; Linda R. Petzold: Computer Methods for Ordinary Differential Equations and Differential Algebraic Equations, 1998

• J. C. Butcher: Numerical Methods for Ordinary Differential Equations, Wiley, 2003

• Peter Deuflhard & Folkmar Bornemann: Scientific Computing with Ordinary Differential Equations, Springer, 2002

• E. Hairer; S.P. Nørsett; G. Wanner: Solving Ordinary Differential Equations I. Nonstiff Problems. Springer, 2nd Ed., 2000

• E. Hairer; G. Wanner: Solving Ordinary Differential Equations II. Stiff and Differential Algebraic Problems. Springer, 2nd Ed., 2002

• Randall J. LeVeque: Finite Difference Methods for Ordinary and Partial Differential Equations. SIAM, 2007

Lectures - Runge-Kutta methods

Lecture 01 - Introduction to one-step methods (Runge-Kutta methods)

Lecture 02 - Explicit Runge-Kutta methods

Lecture 03 - Order conditions, stability, and Runge-Kutta methods

Lecture 04 - Adaptive step-size control and Runge-Kutta methods

Lecture 05 - Implementation of implicit Runge-Kutta methods

Lecture 06 - Runge-Kutta methods for event based systems, index-1 DAEs, and PDEs

Assignments

Assignment 1 - Runge-Kutta Methods