2026-10-14T19:33:17Zhttps://www.radar-service.eu/oai/OAIHandler

10.35097/13342026-10-09T10:59:21Zradar4kit

https://dx.doi.org/10.35097/1334 Carle, Constantin Numerical experiments to "On leapfrog-Chebyshev schemes for second-order differential equations" Karlsruhe Institute of Technology 2023 Mathematics dataset Dataset info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-sa/4.0/legalcode 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. The computations are done with Python3. ##### Requirements 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) ##### Generation of figures 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. 10.5445/IR/1000147744 KITopen-DOI application/x-tar