Semi-implicit Euler method: Difference between revisions

Revision as of 19:11, 2 March 2007

Revision as of 12:13, 3 March 2007

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TheIn mathematics, the '''Euler-Cromer algorithm''' is a modification of the [[Euler approximationintegration|Euler method]] for solving [[numericalordinary integrationdifferential equation]]s. whichIt gives much better results for [[Oscillation|oscillatory]] solutions.

Given a pair of [[differential equation]]s of the form

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and initial conditions

:<math> (x_0,v_0), \quad</math>

the Euler-Cromer algorithm produces an approximate [[Discrete mathematics|discrete]] solution is given by iterating

:<math> v_{n+1} = v_n + a_n \Delta t \quad</math>

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:<math> x_{n+1} = x_n + v_{n+1} \Delta t \quad</math>

where '''<math> \Delta t </math>''' is the timestep.

== See also ===

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* [[Numerical ordinary differential equations]]

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[[Category:Numerical differential equations]]