       Re: Re: NDSolve to solve a set of "loop" equations

• To: mathgroup at smc.vnet.net
• Subject: [mg101387] Re: [mg101374] Re: NDSolve to solve a set of "loop" equations
• From: Haibo Min <yshdfeng at gmail.com>
• Date: Sat, 4 Jul 2009 06:43:30 -0400 (EDT)
• References: <h2i4rd\$94c\$1@smc.vnet.net> <200907030939.FAA19308@smc.vnet.net>

```Thanks Pillsy, a really elegant express!

Best regards,
haibo

On Fri, Jul 3, 2009 at 5:39 PM, Pillsy <pillsbury at gmail.com> wrote:

> On Jul 2, 7:14 am, Haibo Min <yshdf... at gmail.com> wrote:
> > Hi, there.
>
> > I am new to mathematica and recently I am intrigued by the convenience of
> > NDSolve function, since there is no need to write the Runge-kutta like
> > functions myself to solve ODEs. However, if what I want to solve is a
> lis=
> t
> > of equations expressed in a loop way, I have no idea how to express it.
>
> > For example, a set of simple equations are:
> > Subscript[y, i]'[x]  = Subscript[y, i][x] Cos[x + Subscript[y, i][x]]=
>  + i,
> > where i=1,2,...,N;
>
> This is almost certainly not what you want, because, like in a few
> other languages, "=" is an assignment operatore, whereas "==" is the
> test for equality. So instead you'd want
>
> Subscript[y, i]'[x] == Subscript[y, i][x] Cos[x + Subscript[y, i][x]]
> + i
>
> In order to create a list of these, for i rangeing from 1...n, you
> want to use Mathematica's Table construct. This function will generate
> a list of n equations, for a positive integer n:
>
> eqns[n_Integer] /; Positive[n] :=
>  Table[Subscript[y, i]'[x] == Subscript[y, i][x] Cos[x + Subscript[y,
> i][x]] + i, {i, n}];
>
> HTH,
> Pillsy
>
>

```

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