Programming methods

This part exposes our technical and algorithmical choices, the implementation and the numerical resolution of our models.

Models implementation

All our models are using the Python language. Python has several major perks:

• Very good floating numbers management
• High level programming
• Object-oriented
• Not an exclusively numerical tool, which allows much more options than Scilab or Matlab

Numerical resolution of ODEs

We chose not to use the resolution functions included in Scipy to have more coding liberties.
To solve our ODEs, we used a simple Euler method. Here is an example:
Let the following be a Cauchy problem:

Considering the following Taylor expansion:


Let us define the sequence such as and
And thus, the sequence such as and
Thus, we can define the Euler method:

Which, standardized, becomes .

In the end, all our differential equation systems are implemented like so:

where N is the number of equations in the system.

This is how we implemented the equation systems in Python. The fact that we didn't use ODE-solving libraries allowed us to introduce definition domains for some variables, which improved the overall stability in numerical resolutions.
For a simpler and quicker use of repetitive tasks, we also encapsulated everything in a class scheme.

Display

We used the Matplot library to display 2D and 3D curves.