Talk:Semi-implicit Euler method: Difference between revisions

Revision as of 21:41, 6 March 2007

Revision as of 06:36, 7 March 2007

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:In every example I have ever seen, the Euler method leads to an ''increase'' in energy. I am not 100% confident that this will always be the case, but I suspect it may be so. Either way I don't think it is appropriate to say that the Euler method "often" leads to decreasing energy.--[[User:DJIndica|DJIndica]] 21:41, 6 March 2007 (UTC)

I removed the fact that Euler-Cromer performs well for oscillatory functions because I have a hard time believing it. You say that Giardano's book does not give any evidence, and the only evidence from the Delaware web page is that it works well for the harmonic oscillator. However, the good performance for the harmonic oscillator is explained by the fact that Euler-Cromer is a symplectic method and the harmonic oscillator is a Hamiltonian system. I don't see a reason why Euler-Cromer would perform well for non-Hamiltonian oscillators.

You're right that the Euler method usually increases energy. That was a mistake on my part, now fixed. Thanks for noticing that. -- [[User:Jitse Niesen|Jitse Niesen]] ([[User talk:Jitse Niesen|talk]]) 06:36, 7 March 2007 (UTC)