For my coursework I've been told to write an algorithm in Python to solve the Euler-Lagrange equations with Dirichlet boundary conditions.
This is my first Numerical Methods module. We have briefly covered finite difference methods for PDE's but not for an equation this complex.
To be precise, the Lagrangian I have been given is:
$$ \alpha (\dot y) ^2 +\beta(t^2-1)(\dot y) ^3 -y $$
With boundary conditions: $y(0)=1 , y(1)=0.9 $. I have been told that we must compute all derivatives numerically.
What algorithm would you recommend, I'm lost on where to start so any help is very much appreciated.
Thank you!