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Re: Re: Manipulate a NDSolve equation is it possible

• To: mathgroup at smc.vnet.net
• Subject: [mg105609] Re: [mg105602] Re: Manipulate a NDSolve equation is it possible
• From: DrMajorBob <btreat1 at austin.rr.com>
• Date: Fri, 11 Dec 2009 04:17:51 -0500 (EST)
• References: <hfnv37$gg4$1@smc.vnet.net> <200912100959.EAA25371@smc.vnet.net>
• Reply-to: drmajorbob at yahoo.com

This does the integration once (symbolically), rather than all over again  
(numerically) every time r, c, or v0 is changed:

Clear[i, v, v0, r, c]
i[t_] = Boole[10 <= t <= 60];
v[r_, c_, v0_, t_] =
   v[t] /. First@
     Assuming[{-80 <= v0 <= -50, 1/10 <= c <= 10, , 1/10 <= r <= 10},
      DSolve[{v'[t] == 1/c (i[t] - v[t]/r), v[0] == v0}, v, t]];
Manipulate[
  Plot[v[r, c, v0, t], {t, 0, 100}, PlotRange -> {{0, 100}, {-80, 10}},
    PlotStyle -> {Blue, Thick}, Frame -> True], {r, 0.1, 10}, {c, 0.1,
   10}, {v0, -80, -50}]

Bobby

On Thu, 10 Dec 2009 03:59:27 -0600, Albert Retey <awnl at gmx-topmail.de>  
wrote:

> Hi,
>
>> Can the following be made interactive?  I would like my students to see
>> there results quickly when changing certain values such as the  
>> resistance
>> and capacitance.
>
> sure it can. This is one simple possibility:
>
>
> i[t_] := If[t < 10 || t > 60, 0, 1];
>
> RCSoln[R_, c_:1, v0_:-70] :=
>  NDSolve[{v'[t] == 1/c (i[t] - v[t]/R), v[0] == v0}, v, {t, 0, 100}]
>
> Manipulate[
>  Plot[Evaluate[v[t] /. RCSoln[r, c, v0]], {t, 0, 100},
>   PlotRange -> {{0, 100}, {-80, 10}}, PlotStyle -> {Blue, Thick},
>   Frame -> True],
>  {r, 0.1, 10},
>  {c, 0.1, 10},
>  {v0, -80, -50}
>  ]
>
>
> hth,
>
> albert
>


-- 
DrMajorBob at yahoo.com

• References:
  • Re: Manipulate a NDSolve equation is it possible
    • From: Albert Retey <awnl@gmx-topmail.de>