KIT | KIT-Bibliothek | Impressum | Datenschutz

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

Carle, Constantin; Hochbruck, Marlis [Beteiligte*r]

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.


Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsdaten
Publikationsdatum 17.06.2021
Erstellungsdatum 14.06.2021
Identifikator DOI (KIT): 10.5445/IR/1000133907
KITopen-ID: 1000133907
Lizenz Creative Commons Namensnennung – Nicht kommerziell – Weitergabe unter gleichen Bedingungen 4.0 International
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Externe Relationen Siehe auch
Schlagwörter time integration, second-order ode, leapfrog method, stability analysis, error analysis, Hamiltonian systems, CFL condition, Chebyshev polynomials, wave equation
Liesmich

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.

Art der Forschungsdaten Dataset
KIT – Die Forschungsuniversität in der Helmholtz-Gemeinschaft
KITopen Landing Page