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MathGroup Archive 1998

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Re: Need help plotting multiple NDSolve solutions


  • To: mathgroup@smc.vnet.net
  • Subject: [mg10689] Re: Need help plotting multiple NDSolve solutions
  • From: Norbert Scherm <scherm@irt.uni-hannover.de>
  • Date: Fri, 30 Jan 1998 04:24:26 -0500
  • Organization: Inst.f.Regelungstechnik Uni.-Hannover
  • References: <6a1q24$q4n@smc.vnet.net>

Van Graves wrote:
> 
> Hi, I'm a new Mathematica user and would like to plot a "family" of
> solutions for a set of simultaneous differential equations using
> multiple sets of initial conditions.  I couldn't find an example in any
> of the online documentation or on the Wolfram web site.  Can anyone
> give me an example of how to do this?

Fortunately, these days I dealt with a similar problem  (varying
parameters of the ODE).  

-----------------------------------------------------------

dfeld={(*
       0.001,
       0.1,
       0.2,
       0.3,*)
       0.4,
       0.5,
       0.6,
       0.7,
       0.8,
       0.9(*,
       1.0,
       1.5,
       2.0,
       3.0,
       4.0,
       5.0*)}; 

Clear[y,x,d,Te];

For[i=1,i<=Dimensions[dfeld][[1]],i++,
  Print[Dimensions[dfeld][[1]]-i];
  d=dfeld[[i]];
  Te=2.0*Pi*1.75;
  result=
  NDSolve[
    {x''[t]+2*d*x'[t]+x[t]==1.0,
     x'[0]==0,
     x[0]==0
    },x,{t,0,Te}];
    y[i]=(x/.result)[[1]];
 g[i]=Plot[Evaluate[x[t]/.result],{t,0.0,Te},DisplayFunction->Identity];
];
Show[
  Table[ g[i],{i,Dimensions[dfeld][[1]]} ],
  DisplayFunction->$DisplayFunction
]

-----------------------------------------------------------


Instead of the parameter `d=dfeld[[i]]' you have to vary the  initials
in each iteration of the loop. 

I hope this helps...

(Norbert)



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