Talk:Heun's method

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[edit] Tableau

The Butcher tableau does not correspond with the equation; the tableau corresponding to the equations is

0
1 1
1/2 1/2

Furthermore, I always thought that Heun's method refers to the three-stage third-order method (sorry, I'm too lazy to format it correctly)

 0  |
1/3 | 1/3
2/3 |  0  2/3
----+-------------
    | 1/4  0  3/4

I'll try to consult some books next week. -- Jitse Niesen (talk) 12:39, 14 June 2007 (UTC)

You are absolutely right on the tableau-bug, that was copy and paste that went on too quickly. With regard to which method is Heun's, I've seen both (now that you have reminded me), but the simpler one is prominent, as also a quick google search confirms. Though I suppose both can be mentioned in this article. --Berland 20:49, 14 June 2007 (UTC)

[edit] Heun's method is not the modified Euler's method!

In all my textbooks (they are in Italian, but for what I saw the used language is the same as English, unlike for calculus), I can find that while Heun's method has equation:

u_{n+1} = u_n + \frac{h}{2} \left( (f(t_n, u_n) + f(t_{n+1}, u_n + h f(t_n, u_n)) \right)

like in the article, while modified Euler's method has equation:

u_{n+1} = u_n + h f(t_n + \frac{h}{2}, u_n + \frac{h}{2} f(t_n, u_n))

with tableau:

0
1/2 1/2
0 1

So, I consider what the article claims ("Heun's method is also sometimes called the modified Euler method.") simply as an error. I'm correcting the article myself, but I'm mentioning it here to allow being corrected. --Blaisorblade (talk) 14:35, 3 February 2008 (UTC)