Differential Algebraic Equations: Solving constrained differential equations in Python

In practical problems involving differential equations, we often find situations where we have a system of ODEs constrained by a number of algebraic equations. Fortunately, there are solvers available to handle these differential algebraic equations. We will look at solving a simple model of a battery using Pythons ODE solver. We will see how problems arise dealing with the constraints and how a DAE solver (We will use Assimulo here) can simplify things.

Wikipedia article on differential algebraic equations: https://en.wikipedia.org/wiki/Differential-algebraic_system_of_equations

Assimulo Website: https://jmodelica.org/assimulo/

Sundials: https://computing.llnl.gov/projects/sundials

IDA Documentation: https://computing.llnl.gov/projects/sundials/ida

Github: https://github.com/kpmooney/numerical_methods_youtube/tree/master/dae

Tip Jar: http://paypal.me/kpmooney