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

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.

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.

##  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.

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.