Talk:Explicit and implicit methods: Difference between revisions

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Latest revision as of 04:07, 14 February 2024

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==Untitled==

Oleg Alexandrov's changes to my last edit improve the article.

On two minor points I disagree, and have reverted:

Line 29 ⟶ 30:

...I'm also told that one only ever *uses* implicit methods when you're seeking a final steady state, since you know when you've found the right answer. This is plainly not true, but again, could someone comment on their use in strongly time-dependent systems? [[User:7daysahead|7daysahead]] ([[User talk:7daysahead|talk]]) 21:51, 10 July 2010 (UTC)

== No Exact Solution? ==

I object to the statement "In the vast majority of cases, the equation to be solved when using an implicit scheme is much more complicated than a quadratic equation, and no exact solution exists". In typical cases, an exact solution certainly exists, but there is just not a formula to compute it. The wording of the end of the sentence should to changed as to not be confusing. <span style="font-size: smaller;" class="autosigned">—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/208.120.216.154|208.120.216.154]] ([[User talk:208.120.216.154|talk]]) 02:26, 5 October 2010 (UTC)</span><!-- Template:UnsignedIP --> <!--Autosigned by SineBot-->

:Indeed, I made some changes now. [[User:Nicob1984|Nico]] ([[User talk:Nicob1984|talk]]) 07:49, 8 April 2014 (UTC)

==Assessment comment==

{{Substituted comment|length=215|lastedit=20070428114640|comment=Pretty decent. Needs more on how to solve the equation for implicit methods, connection with stability, PDE methods. -- [[User:Jitse Niesen|Jitse Niesen]] ([[User talk:Jitse Niesen|talk]]) 11:46, 28 April 2007 (UTC)}}

Substituted at 14:51, 29 April 2016 (UTC)

== Some bigger edits planned ==

I am new to editing on Wikipedia, and just wanted to give a heads up for some major edits I intend to make on this article. Hopefully we can start a discussion.

I will introduce the standard initial value problem in the introduction, <math>y'(t) = f(t,y(t)), \quad y(0) = y_0</math>. Currently there are letters <math>F</math>, <math>G</math> being used in conflicting contexts, and the letters <math>F</math>, <math>G</math>, and <math>Y</math> are abandoned after this section. I'll also move the IMEX discussion till later.

In the section "Illustration using the forward and backward Euler methods", I think we should stick to the abstract IVP instead of the quadratic right hand side. While I think specific right hand sides can be useful, I don't think the entire section should be about it. Maybe ultimately the example right hand side could be it's own section.

I do agree with the pedagogical choice of sticking with simple methods such as implicit euler and explicit euler, especially for the IMEX example. However, there are also already articles about implicit and explicit Euler, so we shouldn't spend too much time repeating information about these. We should really focus on essential differences and advantages between implicit and explicit methods.

I have a problem with including Crank-Nicolson in a section all about Euler, and with the statement "Crank Nicolson can be viewed as a form of more general IMEX (Implicit-Explicit) schemes." I have never seen the interpretation of CN as an IMEX method. It is usually viewed as an implicit method, but it CAN be used as the implicit component of an IMEX method, such as Crank-Nicolson/Adams Bashforth 2 (CN/AB2), or Crank-Nicolson/Leapfrog(CNLF). We should have second order examples though, so maybe we just change the name of the section.

Let me know what you think.

[[User:Fish sounds|Fish sounds]] ([[User talk:Fish sounds|talk]]) 13:56, 2 August 2020 (UTC)