2026-08-05T05:32:35Zhttps://www.radar-service.eu/oai/OAIHandler10.35097/12872023-11-15T14:45:26Zradar4kit
10.35097/1287
Dörich, Benjamin
Benjamin
Dörich
0000-0001-5840-2270
Numerical experiments to "On averaged exponential integrators for semilinear wave equations with solutions of low-regularity"
Karlsruhe Institute of Technology
2021
2023
Mathematics
highly oscillatory problems
error bounds
order-reduction
time-integration
second-order evolution equations
filter functions
summation-by-parts formula
Open Access
Creative Commons Attribution Non Commercial Share Alike 4.0 International
Dörich, Benjamin
0000-0001-5840-2270
Buchholz, Simone
Hochbruck, Marlis
This code was used for the numerical experiments in the preprint (CRC Preprint 2021/12; URL: https://www.waves.kit.edu/downloads/CRC1173_Preprint_2021-12.pdf) and in the paper "On averaged exponential integrators for semilinear wave equations with solutions of low-regularity" by S. Buchholz, B. Dörich, and M. Hochbruck.
This program is intended to reproduce the results from the paper
"On averaged exponential integrators for semilinear wave equations with solutions of low-regularity. "
by S. Buchholz, B. Dörich, and M. Hochbruck.
The codes generates Figure 2.
#### Requirements
The program is tested with
1) Ubuntu 16.04.7 LTS and Python 3.7.6 and the following version of its modules:
- numpy - 1.15.4
- scipy - 1.4.1
- matplotlib - 3.2.1
- tikzplotlib - 0.9.6
2) Ubuntu 18.04.5 LTS and Python 3.6.9 and the following version of its modules:
- numpy - 1.19.2
- scipy - 1.5.1
- matplotlib - 3.3.2
- tikzplotlib - 0.9.4
#### Figure 2
In this folder open a console and run the following commands after each other.
1) Run "python3 run_paper_Strang_N_2pw09.py"
2) Run "python3 run_paper_Strang_N_2pw10.py"
3) Run "python3 run_paper_Strang_N_2pw11.py"
After running the calculations, the errors can be found in the folder "results" as tikz-files.
10.5445/IR/1000130367
application/x-tar