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Re: Coupled Differential Equations


"Cyrill Slezak" <Cyrill.Slezak at Physik.Uni-Augsburg.DE> wrote in message news:<adkf9d$9u8$1 at smc.vnet.net>...
> I understand that NDSolve will solve a set of first order coupled. diff.eqn.
> Here is my problem: I have a set of 20+ equation that all have the exact
> same structure and I can't seem to find an easy way to input them. For any
> help I'd be highly appreciative. The equations are of the form
> 
> d V_k(l)/d l = V_k(l) + Sum[ V_k'(l), (k not equal k')]
> 
> where k is the number of diff. eqn.
> 
> Thanks for any help,
> 
> Cyrill

Hello,

You may write your system as:
   d V_k(x) /d x = Sum[ V_m(x),{m=1,nmax}]
Then
d V_1(x)/d x  =d V_2(x)/d x  =d V_3(x)/d x  = . . .
and
V_2(x) = V_1(x) + C_2
V_3(x) = V_1(x) + C_3
   . . .
substitute to equation we receive:
V_1(x) = C_1 * Exp[ n*x ] -(C_2 + C_3 + ... + C_nmax) / nmax
with previos equals it is a general solution.
                               Nodar Shubitidze


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