2026-04-20T16:45:49Zhttps://www.radar-service.eu/oai/OAIHandler10.35097/15122023-11-15T14:45:24Zradar4kit
10.35097/1512
Carle, Constantin
Constantin
Carle
Numerical experiments to "Error analysis of multirate leapfrog-type methods for second-order semilinear odes"
Karlsruhe Institute of Technology
2021
2023
Mathematics
time integration
second-order ode
leapfrog method
stability analysis
error analysis
Hamiltonian systems
CFL condition
Chebyshev polynomials
wave equation
Open Access
Creative Commons Attribution Non Commercial Share Alike 4.0 International
Carle, Constantin
Hochbruck, Marlis
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.
10.5445/IR/1000133907
application/x-tar