## 02685 Scientific Computing for Differential Equations02685 Scientific Computing for Differential Equatons is given in the spring semester In that course, I give 6 lectures related to Runge-Kutta methods for systems of differential equations. ## References and BooksMichael 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 |