Wikipedia:Reference desk/Archives/Mathematics/2014 July 13

= July 13 =

Efficient numerical integration
Runge kutta methods provide an excellent solution to systems of the form $$\dot{x}_i = f_i\left( \{ x \} \right)$$ but does anyone know of a good numerical recipe for solving $$\sum_j g_{ij}\left( \{ x \} \right) \dot{x}_j = f_i\left( \{ x \} \right)$$ without having to invert the matrix $$g_{ij}$$ at every time step? — Preceding unsigned comment added by 84.92.32.38 (talk) 14:24, 13 July 2014 (UTC)
 * This isn't a huge help but I think really you only need to solve the equations for the $$\dot{x}_j$$, which is somewhat easier that finding the inverse of the matrix. Suppose there were a more efficient method for generating a solution. Then you could apply it the case where the g's are constant, and from the solution you could determine the $$\dot{x}_j$$, which would then give you a more efficient method for sets of linear equations. So, and it would nice if someone checked my reasoning here, finding the solution of the differential equation must be at least as hard as solving systems of linear equations. Perhaps there is some good news though in that there are iterative methods for solving linear equations. So you could use the solution at point k as the starting point for the iteration at point k+1 and since presumably the solutions are close you may only need one or two iterations to get an accurate result. That assumes that the g is smooth and well conditioned. Of course everything here assumes g is nonsingular.--RDBury (talk) 16:11, 13 July 2014 (UTC)

I need a little help
How do you do this problem? 5`7-6 — Preceding unsigned comment added by 66.87.65.238 (talk) 23:49, 13 July 2014 (UTC)


 * What does that operator between 5 and 7 mean?--Jasper Deng (talk) 03:28, 14 July 2014 (UTC)


 * Now that is an interesting question! I can't find any real use of it as a mathematical operator. ` mentions use in LaTeX for quotations, and also mentions use as command substitution in e.g. Bash shell. None of those make sense here though... SemanticMantis (talk) 15:18, 14 July 2014 (UTC)


 * Could be a mistake for an uparrow, meaning 5 to the power 7 (minus 6, which for all I know is meant to be combined with the 7 rather than deducted last).→86.146.61.61 (talk) 18:56, 14 July 2014 (UTC) g

exactly what does operator mean


 * Is that supposed to be a multiplication sign, division sign, or something else ? StuRat (talk) 00:54, 15 July 2014 (UTC)


 * We want to know what the apostrophe in your problem means. What is the context of your problem? K ati e R  (talk) 12:49, 15 July 2014 (UTC)


 * For clarification, and reference apostrophe is this: ' -- grave accent or backtick is this: ` (which is what is in the original problem, but the two are often confused. There is also the Prime (symbol), which can mean a few things, but none are relevant here. (I also thought 5`7-6 might be the number of a problem in some book, but we'd need to know what the problem is...) SemanticMantis (talk) 15:17, 15 July 2014 (UTC)


 * Don't spend time on this. Somebody is just having a little fun watching everybody scratching their heads. Even the most inexperienced poster in the whole world would realize that the problem is totally incomprehensible. YohanN7 (talk) 15:25, 15 July 2014 (UTC)
 * (Duly noted. But I can't be trolled. I WP:AFG, and only post when I'm having fun ;) SemanticMantis (talk) 15:37, 15 July 2014 (UTC)