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Numerical experiments to "error analysis of exponential integrators for nonlinear wave-type equations"

Abstract: This code has been used for the numerical experiments in the thesis "Error Analysis of Exponential Integrators for Nonlinear Wave-Type Equations" by Benjamin Dörich, see https://www.doi.org/10.5445/IR/1000130187. TechnicalRemarks: ## Readme

This program is intended to reproduce the results from the thesis "Error Analysis of Exponential Integrators for Nonlinear Wave-Type Equations" by Benjamin Dörich

Requirements

The program is tested with

1) Ubuntu 16.04.7 LTS and Python 3.7.6 and the following version of its modules: - numpy - 1.15.4 - scipy - 1.4.1 - matplotlib - 3.2.1 - tikzplotlib - 0.9.6 (quasilinear only:) - dolfin - 2018.1.0 - fenics - 2018.1.0

2) Ubuntu 18.04.5 LTS and Python 3.6.9 and the following version of its modules:

  • numpy - 1.19.2
  • scipy - 1.5.1
  • matplotlib - 3.3.2
  • tikzplotlib - 0.9.4 (quasilinear only:)
  • dolfin - 2019.2.0.dev0
  • fenics - 2019.2.0.dev0
Figure 4.2

In the folder "semilinear_low_reg/Fig_convergence" open a console and run the following commands after each other.

1) Run "python3 run_diss_Strang_N_2pw09.py" 2) Run "python3 run_diss_Strang_N_2pw10.py" 3) Run "python3 run_diss_Strang_N_2pw11.py"

After running the calculations, the errors can be found in the folder "results" as tikz-files.

Figure 4.3

In the folder "semilinear_low_reg/Fig_inner_filter" open a console and run the following commands after each other.

1) Run "python3 run_diss_Strang_N_2pw09.py" 2) Run "python3 run_diss_Strang_N_2pw10.py" 3) Run "python3 run_diss_Strang_N_2pw11.py"

After running the calculations, the errors can be found in the folder "results" as tikz-files.

Figure 7.1

In the folder "quasilinear_expo" open a console and run the following commands after each other.

1) Run "python3 1_generate_initial_matrices.py" 2) Run "python3 2_diss_run_reference_solution.py" 3) Run "python3 3_diss_run_Euler_X.py" 4) Run "python3 4_diss_run_Euler_Y.py" 5) Run "python3 5_diss_run_midpoint.py"

After running the calculations, the errors can be found in the folder "quasilinear_expo/extracted_data/". (a) settings_ contains the information of the config file (b) infos_ contains the computed errors (c) plot_* contains a tikz-file which gives the plot for the Euler and the midpoint rule separately.

Cite this as

Dörich, Benjamin (2023). Dataset: Numerical experiments to "error analysis of exponential integrators for nonlinear wave-type equations". https://doi.org/10.35097/1284

DOI retrieved: 2023

Additional Info

Field Value
Imported on August 4, 2023
Last update August 4, 2023
License CC BY-NC-SA 4.0 Attribution-NonCommercial-ShareAlike
Source https://doi.org/10.35097/1284
Author Dörich, Benjamin
Source Creation 2023
Publishers
Karlsruhe Institute of Technology
Production Year 2021
Publication Year 2023
Subject Areas
Name: Mathematics