Numerical experiments to "on leapfrog-chebyshev schemes for second-order differential equations"

Abstract: This code has been used for the numerical experiments in the thesis "On leapfrog-Chebyshev schemes for second-order differential equations" by Constantin Carle; see https://www.doi.org/10.5445/IR/1000147725. TechnicalRemarks: The computations are done with Python3.

The code is tested on Ubuntu 20.04.4 LTS with Python 3.8.10 and the following versions of its modules

    numpy           -   1.17.4
    scipy           -   1.3.3
    h5py            -   2.10.0
    dolfin (fenics) -   2019.2.0.dev0 (including mshr)
    matplotlib      -   3.1.2
    tikzplotlib     -   0.9.6 (only for generating tikz/pgfplots files)

Figures 4.6, 4.7, 4.8, 4.9, 4.10, 5.3, 5.4, 5.5, 5.7 (including 5.6), and 5.8 can be generated with this code. In order to obtain Figure X.Y either - execute the Python script script_Figure-XpY.py in a suitable integrated development environment or - run the command python3 script_Figure-XpY.py in a terminal session.

The scripts for Figures 4.6, 4.8, 4.10, and 5.5 only produce half of the figures. To get the other half, open the script and set the Boolean variable at the beginning of the script from True to False (case sensitive).

• Figure 4.6: Boolean variable LFC_unstab
• True : Figures 4.6 (a), (c), (e), (g)
• False: Figures 4.6 (b), (d), (f), (h)
• Figure 4.8: Boolean variable stepsize_small
• True : Figures 4.8 (a), (b)
• False: Figures 4.8 (c), (d)
• Figure 4.10: Boolean variable LFCpol_to_G
• True : Figures 4.10 (a), (b), (c)
• False: Figures 4.10 (d), (e), (f)
• Figure 5.5: Boolean variable stepsize_small
• True : Figures 5.5 (a)
• False: Figures 5.5 (b)

Instead of the plots you can get the tikz/pgfplots files which were used for the figures in the thesis by setting the Boolean variable plot_figure from True to False in the scripts.