Affine Covariant Newton
Make use of the new affine covariant Newton algorithm to find roots of large systems of equations.
Discretize the nonlinear differential equation 
with a finite difference method.
Set up the Jacobian of the discretized system of equations.
Set up an initial seed for the root-finding algorithm.
Inspect the number of steps, evaluations and Jacobian evaluations needed to find the root of the system of equations.
Compare that to the newly implemented affine covariant Newton method
The affine covariant Newton method significantly reduces the number of Jacobian evaluations needed to find the root. Since the construction and evaluation of the Jacobian can be time consuming for large systems of equations, the affine covariant Newton method helps in speeding up the root-finding process.
More details about the affine covariant Newton method can be found in the documentation.
