Lecture "Numerical Analysis of Differential Equations" (WS 2025/2026)

Jun.-Prof. Dr. Mira Schedensack
Universität Leipzig
Fakultät für Mathematik und Informatik
Mathematisches Institut

Participants:

This lecture is suitable for students in mathematics (Bachelor, Master, Diploma) and in mathematical physics with the standard knowledge from the introductory lectures and functional analysis. It is possible to attend the lecture functional analysis in parallel.

Content:

Differential equations play an important role in many applications. However, it is usually not possible to find a formula for the exact solution. In this lecture, numerical schemes that approximate the solutions are discussed. The lecture is composed of three parts: The first part is devoted to numerical approximations of ordinary differential equations, the second to finite difference methods of time-dependent partial differential equations, while the third part discusses finite element methods for partial differential equations.

Time of lectures

The lecture will take place on Monday at 09:15-10:45 and Tuesday at 09:15-10:45 and the tutorial classes will take place on Monday at 11:00-12:30. The lecture and the tutorial class will be in SG 3-14.

News

The lectures on 2. and 3. February have to be cancelled.

For health reasons, the lectures on 27th and 28th October have to take place as self-study. Please read the new version of the lecture notes for this purpose. The tutorial class is cancelled and exercise sheets 1 and 2 will be discussed in the tutorial class on 3rd November.

For health reasons, the lectures on 20 and 21 October and the tutorial class on 20 October have to be cancelled.

The first lecture will take place on Monday, October 13 at 09:15.

Material

Exercises
 Number   Exercise Sheet   Discussion on   code   remarks 
1 Exercise Sheet 1 03.11.2025 The date for the discussion has changed again.
2 Exercise Sheet 2 03.11.2025   ODE_solver.jl 
3 Exercise Sheet 3 10.11.2025
4 Exercise Sheet 4 17.11.2025  ODE_solver_2.jl    The code is the solution for Sheet 3 including the classical Runge-Kutta scheme. 
5 Exercise Sheet 5 24.11.2025
6 Exercise Sheet 6 1.12.2025
7 Exercise Sheet 7 8.12.2025 In Exercise 1.3, the Delta x was changed to (Delta x)^2.
8 Exercise Sheet 8 15.12.2025
9 Exercise Sheet 9 5.01.2026
10 Exercise Sheet 10 12.01.2026
11 Exercise Sheet 11 19.01.2026 The P2 part of exercise 2 was deleted. Exercise 3 has been corrected.
12 Exercise Sheet 12 26.01.2026
Code
code for introduction

code for heat equation

code for transport equation

wave_explicit.m

wave_implicit_naive.m

wave_implicit_CN.m

triangulation_square.m

red_refine.m

FEM.m

runFEM.m

Lecture Notes
Lecture Notes (current version)

A German version of the lecture notes can be found at the webpage Numerik 2. Note that this version is not updated.