Forward and Backward Euler and Crank-Nicolson

solvers = [
    odespy.ForwardEuler(f),
    # Implicit methods must use Newton solver to converge
    odespy.BackwardEuler(f, nonlinear_solver='Newton'),
    odespy.CrankNicolson(f, nonlinear_solver='Newton'),
    ]

Two plot types:

• \( u(t) \) vs \( t \)
• Parameterized curve \( (u(t), v(t)) \) in phase space
• Exact curve is an ellipse: \( (I\cos\omega t, -\omega I\sin\omega t) \), closed and periodic