The difference with the standard Euler method is that the Euler–Cromer method uses <math>v_{n+1}</math> in the equation for <math>x_{n+1}</math>, while the Euler method uses <math>v_n</math>.
The Euler–Cromersemi–implicit methodEuler is a [[Numerical ordinary differential equations#Consistency and order|first-order integrator]], just as the standard Euler method. This means that it commits a global error of the order of Δt. However, the Euler–Cromersemi–implicit Euler method is a [[symplectic integrator]], unlike the standard method. As a consequence, the Euler–Cromersemi–implicit Euler method almost conserves the energy (when the Hamiltonian is time-independent). Often, the energy increases steadily when the standard Euler method is applied, making it far less accurate.
