Semi-implicit Euler method: Difference between revisions

Revision as of 06:34, 7 March 2007

Revision as of 06:36, 7 March 2007

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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–Cromer method is a [[Numerical ordinary differential equations#Consistency and order|first-order integrator]], just as the standard Euler method. This means that it commits ana global error of the order of &Delta;t. However, the Euler–Cromer method is a [[symplectic integrator]], unlike the standard method. As a consequence, the Euler–Cromer 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.

== Example ==