Numerical experiments to "Error Analysis of Exponential Integrators for Nonlinear Wave-Type Equations"

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/extracteddata/".
(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.