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

Abstract: 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. TechnicalRemarks: 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.