Numerical experiments to "on averaged exponential integrators for semilinear wave equations with solutions of low-regularity"

Abstract: 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. TechnicalRemarks: 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.

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

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.