This lecture builts on the lecture “Introduction to Numerical Methods” covering numerical methods for ordinary and partial differential equations. Both theoretical and practical aspects of these methods are covered. The lecture is accompanied by theoretical and practical exercises including programming in C++. The subjects covered are:

• Theory of ordinary differential equations
• One step methods
• Treatment of stiff differential equations
• Multistep methods
• Boundary value problems
• Introduction to partial differential equations
• Finite difference methods

Language

The lecture will be given in English.

Moodle

This course is managed with a Moodle page.

Registration for Exercises

Registration to the exercises is on the Müsli page. The registration will be opened in the first week of the semester.

Lecture Notes

Lecture notes of Guido Kanschat and Robert Scheichl are in english and cover most of the material that I plan to cover. There might differences in the PDE part.

There are notes of the lecture made by Stefan Breuning (in German): Vorlesungsmitschrieb

Here are the complete lecture notes from 2017 in handwriting (also in German): Ipad hand writing (160 MB!)

And there are the lecture notes by Prof. Rannacher published by Heidelberg University Publishing. Unfortunately in german as well.

Material for the Exercises

Styleguide für das Programmieren in C++

HDNum inklusive Dokumentation

Exercise Sheets

Will be released on the Moodle platform.

Literature Hints

• H. R. Schwarz: Numerische Mathematik, Teubner

• R. Rannacher: Vorlesungsskriptum “Numerische Methoden für gewöhnliche Differentialgleichungen”

• A. Quarteroni, R. Sacco, F. Saleri: Numerical Mathematics, Springer

• J. M. Melenk, Vorlesungsnotizen zu “Numerik von Differentialgleichungen”, TU Wien

• E. Hairer, S. Norsett, G. Wanner: Solving Ordinary Differential Equations I, 2nd edition, Springer Verlag, 2009.

Remarks

This lecture is the second lecture of the sequence of numerics lectures and corresponds to module MD1. The lecture is continued by the lecture “Finite Elements” (MH7).

Exam

t.b.a.