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Re: Solution of a non-linear ODE

  • To: mathgroup at smc.vnet.net
  • Subject: [mg81936] Re: Solution of a non-linear ODE
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Sun, 7 Oct 2007 05:29:43 -0400 (EDT)
  • References: <fe7hgc$ok8$1@smc.vnet.net>

Hi,

your second equation is not very helpful because

FullSimplify @@ odesys

gives you a single second order equation for the
two variables u[t] and v[t] and you need a second
second order equation for v[t]. You can try

deq3 = FullSimplify @@ odesys;

odesys1 = {deq3, D[#, t] & /@ eq2}

and

DSolve[
  odesys1, {u[t], v[t]}, t]

Regards
   Jens



sigmundv at gmail.com wrote:
> Distinguished group members,
> 
> I would like you to try the following:
> 
> First define
> 
> f[u_, v_] := 1
> eq1 = D[ArcTan[v'[t]/u'[t]], t] + 1/2 (D[Log[f[u[t], v[t]]], u[t]]
> v'[t]^2 - D[Log[f[u[t], v[t]]], v[t]] u'[t]) == 0;
> eq2 = u'[t]^2 + v'[t]^2 == 1/f[u[t], v[t]];
> odesys = {eq1, eq2};
> ic = {u[0] == 0, v[0] == 0, u'[0] == 0, v'[0] == 1};
> 
> Then try to solve 'odesys', with the initial conditions 'ic', either
> using DSolve or NDSolve, or both. What do you get? For NDSolve I get
> the warning
> 
> Solve::svars: Equations may not give solutions for all "solve" \
> variables.
> 
> and the the input is returned unevaluated.
> 
> When I use NDSolve on the initial value problem, the system runs
> several minutes, without returning any result.
> 
> Can any of you explain this behaviour?
> 
> When doing the same calculations with another similar software
> package, I get solutions easily. Therefore it seems strange that
> Mathematica does not return any solution.
> 
> Best regards,
> Sigmund Vestergaard
> 
> 


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