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