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Re: Solving Simultaneous Differential Equations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg78926] Re: Solving Simultaneous Differential Equations
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Fri, 13 Jul 2007 05:57:33 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, UK
  • References: <f74rj2$80f$1@smc.vnet.net>

Nikhil Shankar wrote:
> Hey guys,
> 
> I'm working on a model of the heart, which can be simplified to eleven simultaneous differential equations... I am solving them all with NDSolve and explicit Runge Kutta numerical integration. I am happy with the results, but I don't know how to plot a single function, of the eleven that are solved simultaneously.
> 
> I can plot all 11 of them on one graph by using 
> 
> Plot[Evaluate[eqs /. %], {t, 0, 10}]
> 
> where eqs are all 11 functions, and the last output was the set of the 11 interpolating functions. Plotting all 11 pretty much has no value to me though.
> 
> How do I store the interpolating function data for each function so I can plot each by itself?
> 
> Also, how can I save step-by-step results using Reap/Sow?
> 
> Thanks for your help guys.
> 

Since you did not provide any example, I can only guess what naming 
convention you used. The following should help you started.

In[1]:=
sols = NDSolve[{Derivative[1][x][t] == -y[t] - x[t]^2,
     Derivative[1][y][t] == 2*x[t] - y[t]^3, x[0] == y[0] == 1}, {x, y},
    {t, 20}]
Plot[Evaluate[{x[t], y[t]} /. sols], {t, 0, 20}]
Plot[Evaluate[{x[t]} /. sols], {t, 0, 20}]
Plot[Evaluate[{y[t]} /. sols], {t, 0, 20}]

Out[1]=
{{x\[Rule]InterpolatingFunction[{{0.,20.}},<>],y\[Rule]InterpolatingFunction[{\
{0.,20.}},<>]}}

Out[2]=
â??Graphicsâ??

Out[3]=
â??Graphicsâ??

Out[4]=
â??Graphicsâ??

Regards,
Jean-Marc




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