Talk:Numerical methods for ordinary differential equations

Names

According to the St Andrews' MacTutor website, specifically http://www-history.mcs.st-and.ac.uk/history/Mathematicians/Runge.html and http://www-history.mcs.st-and.ac.uk/history/Mathematicians/Kutta.html, the names are as written by 142.177.19.200 (Carle David Tolmé Runge and Martin Wilhelm Kutta), and not as I wrote them earlier. Jitse Niesen 15:20, 8 Jan 2004 (UTC)

Gear

I removed the following item from the History section:

1968 - C. William Gear invents the first stable algorithms to solve stiff differential equations.

I suppose this refers to BDF (backward differentiation formula), which were in fact already introduced by Curtiss and Hirschfelder in the same 1952 paper where they talk about stiffness. Please correct me if I am wrong. -- Jitse Niesen (talk) 5 July 2005 16:58 (UTC)

Consistent methods

It seems that the consistence of a method is mentioned in the pages about Runge-Kutta and Adams method, but it is never defined. Is this page the right place to put its definition? Fph 12:41, 21 June 2006 (UTC)

Yes, I think so. It would perhaps fit in nicely in the discussion about order. By the way, benvenuti a Wikipedia! -- Jitse Niesen (talk) 13:37, 21 June 2006 (UTC)

Grazie! I have added some words about consistency (by the way, it seems consistency is more widespread than consistence). Someone should add a short comment about the consistency being a weaker condition than convergence to ensure the method makes (at least some) sense. I'm not sure I know English enough to write it correctly, so I'll better leave it to someone else. :-) --Fph 19:14, 28 June 2006 (UTC)

Slight Change

I think it would make the equations easier to understand if h is replaced by $\Delta x$.

Please comment on my suggestion. --Freiddy 18:48, 2 March 2007 (UTC)

Perhaps (I suppose you mean $\Delta t$). Your notation is indeed makes it easier for the reader to remember that it stands for the step size. On the other hand, expressions like $hf(t,y)$ and $h^{p}$ become slightly more awkward: you get $\Delta tf(t,y)$ (could be misinterpreted, though adding some spacing might remedy this) and $\Delta t^{p}$ (might need parentheses). So, I don't know. -- Jitse Niesen (talk) 03:05, 3 March 2007 (UTC)

$\Delta t^{p}$ is mostly understandable, since most people are quite used to the notation ${\frac {d^{2}f}{dx^{2}}}$. You can also just change $\Delta tf(t,y)$ into $f(t,y)\ \Delta t$ which is just like an integral. --Freiddy 12:28, 3 March 2007 (UTC)