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