Semi-implicit Euler method: Difference between revisions

Revision as of 05:49, 31 May 2008

Revision as of 05:53, 31 May 2008

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== Setting ==

The Euler–Cromersemi–implicit algorithmEuler method can be applied to a pair of [[differential equation]]s of the form

:<math> {dx \over dt} = f(t,v) </math>

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== The method ==

The Euler–Cromersemi–implicit algorithmEuler method produces an approximate [[Discrete mathematics|discrete]] solution by iterating

:<math> v_{n+1} = v_n + g(t_n, x_n) \, \Delta t \quad</math>

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:<math> {dv \over dt} = -{k \over m}x. \quad</math>

The Euler–Cromersemi–implicit algorithmEuler for this equation is

:<math>v_{n+1} = v_n - {k \over m}x_n\Delta t \quad</math>