Datenpaket: Numerical experiments to "Error analysis of multirate leapfrog-type methods for second-order semilinear odes"

This code was used for the numerical experiments in the preprint (CRC Preprint 2021/26; URL: https://www.waves.kit.edu/downloads/CRC1173_Preprint_2021-26.pdf) and in the paper "Error analysis of multirate leapfrog-type methods for second-order semilinear odes" by C. Carle and M. Hochbruck.

The scripts inside the subfolders are intended to reproduce the figures from the preprint > Error analysis of multirate leapfrog-type methods for second-order semilinear ODEs by Constantin carle and Marlis Hochbruck

Requirements

The codes are tested with Ubuntu 20.04.2 LTS and Python 3.8.5 and the following version of its modules:

• numpy - 1.17.4
• scipy - 1.3.3
• dolfin (fenics) - 2019.2.0.dev0 (including mshr)
• matplotlib - 3.1.2
• tikzplotlib - 0.9.6### Generation of figures In the folder "code_figure_6p1-6p2" open a console and run the commands

1. to obatin Figure 6.1 python3 script_figure_2dimEx.py,
2. to obtain Figure 6.2(a) python3 script_figure_FPUT_error.py
3. to obtain Figure 6.2(b) python3 script_figure_FPUT_hamiltonian.py. In the folder "code_figure_6p3" open a console and run the command python3 script_figure_wave-equation.py to obtain Figure 6.3(a) and (b). Additionally to the plots you can get the tikz-files which were used for generating the plots in the pdf by uncommenting the lines #import tikzplotlib #tikzplotlib.save("*****.tikz") at the end of each of the above scripts.