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== Initial discussion ==
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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)
== Method name ==
This is the same thing as semi-explicit Euler, right? Would it anger anyone if suggested the article be renamed to either [[Semi-explicit Euler]] or [[Symplectic Euler]] since those are the names people are familiar with? --[[User:Numsgil|Numsgil]] ([[User talk:Numsgil|talk]]) 18:36, 29 May 2008 (UTC)
Agreed. I was surprised to see this labeled as "semi-implicit" Euler. Under that name I would have expected something like the Crank-Nicolson method. <small class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/24.163.53.10|24.163.53.10]] ([[User talk:24.163.53.10|talk]]) 01:49, 1 October 2015 (UTC)</small><!-- Template:Unsigned IP --> <!--Autosigned by SineBot-->
This name is vague to me, since I've seen semi-implicit Euler to mean many things. Some people call any IMEX semi-implicit Euler, e.g. This is the first time I've seen it used for symplectic Euler. I don't know if the best way to address this is to create multiple sections for the different meanings. [[User:Fish sounds|Fish sounds]] ([[User talk:Fish sounds|talk]]) 02:37, 31 July 2020 (UTC)
Indeed the name is overloaded. At the very least this page should warn readers that there are a large group of people who use this term to mean something else. See for instance the paper "[https://link.springer.com/content/pdf/10.1007/BF01400352.pdf One-step and Extrapolation Methods for Differential-Algebraic Systems]" published in Numer. Math. 51,501-516 (1987).
== Arguments of ''f'' and ''g'' ==
When solving the equations of motion for a damped, driven oscillator the acceleration is a function of both ''x'' and ''v'' and I don't see in principle why the velocity couldn't also be a function of ''x''. I was going to make this change but I wonder if this would have a bearing on whether the system is a Hamiltonian system. Does anyone have any thoughts on this?
I have used this method to obtain solutions for the damped, driven oscillator and the results seem to agree with other methods.--[[User:DJIndica|DJIndica]] ([[User talk:DJIndica|talk]]) 20:40, 2 October 2009 (UTC)
==Assessment comment==
{{Substituted comment|length=197|lastedit=20160510200405|comment=Work out example and add picture, connection with Stormer-Verlet, history. Prose can be tightened. -- [[User:Jitse Niesen|Jitse Niesen]] ([[User talk:Jitse Niesen|talk]]) 13:46, 2 August 2007 (UTC)}}
Substituted at 18:35, 17 July 2016 (UTC)
== Newton–Størmer–Verlet ==
The beginning of the article claims that the semi-implicit Euler method is also called Newton–Størmer–Verlet, but I believe that's incorrect. Newton–Størmer–Verlet (NSV) integration is also known as:
* Størmer–Verlet integration
* Størmer integration
* Verlet integration
* Leapfrog integration
* Encke integration
The Semi-implicit Euler method is not the same as the Verlet method, but the two are related. If your acceleration depends only on position, one step of Verlet integration can be composed from two half steps of Semi-implicit Euler (using one of each of the two variants) <ref name="hairer2003">{{cite journal
| first=Ernst | last=Hairer
| first2=Christian | last2=Lubich
| first3=Gerhard | last3=Wanner
| title=Geometric numerical integration illustrated by the Störmer/Verlet method
| journal = Acta Numerica
| year = 2003
| volume = 12
| pages = 399–450
| doi=10.1017/S0962492902000144
| citeseerx=10.1.1.7.7106
}}</ref> pp.4,5.
[[User:SaltedPretzel|SaltedPretzel]] ([[User talk:SaltedPretzel|talk]]) 08:42, 17 April 2020 (UTC)
{{reflist-talk}}
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