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Minor typo. Replace v_n+1 by x_n+1 |
Jitse Niesen (talk | contribs) →The method: link to energy drift |
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The difference with the standard Euler method is that the semi-implicit Euler method uses ''v''<sub>''n''+1</sub> in the equation for ''x''<sub>''n''+1</sub>, while the Euler method uses ''v<sub>n</sub>''.
The semi-implicit Euler 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 semi-implicit Euler method is a [[symplectic integrator]], unlike the standard method. As a consequence, the semi-implicit Euler method almost conserves the energy (when the Hamiltonian is time-independent). Often, the [[energy drift|energy increases steadily]] when the standard Euler method is applied, making it far less accurate.
== Example ==
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