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Re: Coupled Differential Equations
*To*: mathgroup at smc.vnet.net
*Subject*: [mg34782] Re: [mg34751] Coupled Differential Equations
*From*: Cyrill Slezak <Cyrill.Slezak at Physik.Uni-Augsburg.DE>
*Date*: Thu, 6 Jun 2002 01:55:07 -0400 (EDT)
*References*: <000001c20c72$5d39a860$4b00a8c0@Fischer>
*Sender*: owner-wri-mathgroup at wolfram.com
Curt,
Thank you for your help. It has solved all my initial problems.
Unfortunately I ran into another one, namely adding another equation/set
of eqns. I thought I might just be able to append the list but that did
not seem to work.
If you could tell me what I am doing wrong I would highly appreciate it,
Cyrill
n = 4;
Array[e, n];
For[i = 1, i < n/2 + 1, i++, {e[i] = i*2/n, e[i + n/2] = -i*2/n}]
eqns = Table[\(v \_ k\)'[l] == \(v \_ k\)[l]*(ed[l] - e[k]) +
2* Sum[If[kp == k,
0, \(v \_ kp'\)[
l]*.5/(e[k] - e[kp])*(\(v \_ k\)[l]*
e[kp] + \(v \_ kp\)[l]*e[k])], {kp, 1, n}], {k,
1, n}];
Append[eqns, \(ed\)'[l] == -2*Sum[(\(v \_ k\))^2*(ed[l] - e[k]), {k, 1,
n}]];
vars = Table[\(v \_ k\)[l], {k, 1, n}];
Append[vars, \(ed\)[l]];
NDSolve[eqns, vars, {l, 10}]
>
> Dear Cyrill,
>
> You didn't give very many details of your problem. Therefore I am
> unsure if my answer will help you or not.
>
> Using the function Table[] is one way to do this:
>
> In[1]:= n = 20;
> eqns = Table[\(v\_k'\)[l] == v\_k[l] + \ Sum[If[kp == k,
> 0, \(v\_kp'\)[l]], {kp, 1, n}], {k, 1, n}]
>
> In[2]:= vars = Table[v\_k[l], {k, 1, n}]
>
> In[3]:= DSolve[eqns, vars, l]
>
> I used "kp" instead of your "k'". Hope this helps you.
>
> Curt Fischer
> Dept. of Bioengineering
> Tokyo Institute of Technology
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