Lecture "Numerical Methods for Singularly Perturbed
Differential Equations" (WS 2024/2025)
Jun.-Prof. Dr. Mira Schedensack
Universität Leipzig
Fakultät für Mathematik und Informatik
Mathematisches Institut
Participants:
The lecture is suitable for students in mathematics (Diplom Mathematik
and Diplom Wirtschaftsmathematik) and in mathematical physics with the
standard knowledge from the introductory lectures and from functional
analysis. It is possible to attend the lecture functional analysis in parallel.
Basic knowledge in computational partial differential equations is
helpful, but not necessary.
Content:
Singularly perturbed problems are differential equations
in which the highest derivative appears with a small parameter
ε in front. If ε tends to zero, the
differential equation changes its character. For small
values of ε, the solution exhibits boundary layers
and standard numerical methods fail in the approximation.
This lecture will mainly focus on the singularly perturbed
differential equation
-ε Δ u + b · ∇ u = f
and it will discuss several methods for the numerical
approximation of the solution including
finite difference methods and finite element methods
with upwind, and layer-adapted meshes.
Time of lectures
From 21 October onwards we will start at 9:00.
The lecture will take place on monday from 09:00-10:45 in
A314 and from 11:00-12:15 in SG 3-14. The second lecture
will contain also implementational aspects, exercises,
and interactive elements.
News
The first lecture will take place on monday, October 14 at 9:15.
Material
The lecture is mainly based on the book "Robust Numerical
Methods for Singularly Perturbed Differential Equations"
by H.-G. Roos, M. Stynes, and L. Tobiska.
Code
Finite Differenzen in 1d (Version vom 11.11.2024)
FD2.m (Version vom 10.01.2025)
computeFDsolution.m (Version vom 10.01.2025)