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Re: Rule replacement doesn't work after NDSolve?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg123992] Re: Rule replacement doesn't work after NDSolve?
  • From: gac <g.crlsn at gmail.com>
  • Date: Wed, 4 Jan 2012 05:03:29 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

Thanks very much for the reply.  Your suggestion works as you say, but I'm still confused.  I thought that the replacement is for the function, not the arguments.

> rules must be applied before the arguments are set
> (as is done in the
> plots).
> 

Why, then, does this work? 

sol2 = NDSolve[{y'[t] == 1/x[t]^2, x'[t] == 1/y[t], x[0] == 1, y[0] == 1}, {x, y}, {t, 0, 1}]
y[0.5] /. sol2
x[0.5] /. sol2

One difference I see is that the output in the PDE case has the arguments z,t on the lhs:

{Subscript[x, 1][z,t]->InterpolatingFunction[{{0.,20.},{0.,10.}},<>][t,z],...

But the output in the ODE case does not have the argument on the lhs:

{x->InterpolatingFunction[{{0.,1.}},<>],...

And, if it's a matter of the order of operations, why does this statement also work for the ODE case:

y[t] /. sol2 /. {t -> 0.5}

There's an important difference between the way NDSolve returns in the PDE case and in the ODE case.  I'd like to better understand the difference.

Thanks again for the solution.

Regards.



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