Hi, I have a 4 year experience with python and simulations in python, MATLAB and C. I have previously implemented maxwell's equations (the four basic differential equations in electromagnetics) for various silicon structures and got results close to practical results.
You want to implement some differential equations in python. For debugging, we can use pdb or just simply insert print statements in the code. If there are graphs to be plotted, we can debug using these graphs as well.
For this project, I would suggest installing scipy and matplotlib modules on your systems. These modules are very useful in scientific computing using python.
I will provide proper, readable and easy to use scripts. I will also document them and appropriately comment. If you need to understand how the code works, I will also help with that.
For any clarifications/queries, please contact me. It would also help me if I knew which types of equations you wanted to implement and if there are any methods that you prefer.