Comparison between approaches

• Larger \(h=1.0/\omega\)

• Temporal evolution of \(p^k\)

• Temporal evolution of energy \(E=1/2 m\,(v^k)^2+1/2 K (p^k)^2\)

• True solution , Semi-implicit Euler , Velocity Verlet , Runge-Kutta RK4

• - RK4 loose energy and \(p^k\) converge toward \(l^0\)
• - Symplectic integrator keep oscillating