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MathGroup Archive 1998

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Using NDSolve for matrix equations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg13538] Using NDSolve for matrix equations
  • From: "Eric R. Bittner" <bittner at UH.EDU>
  • Date: Fri, 31 Jul 1998 04:33:46 -0400
  • Organization: university of houston
  • Sender: owner-wri-mathgroup at wolfram.com

I need to solve a set of coupled differential equations  using NDSolve.
The basic form is:

X''[t] == -F[X[t]] + Constraint[X[t],X'[t]]; (basically a mechanical
problem with constraints) No problem if X is a simple scaler.  But,
what if X[t] is a table?   
Still, no problem so long as I can 
expand everything and write it out explicily as eom = {
X1''[t]== -F[X1[t],X2[t],.... ] + ..., X2''[t]== -F[X1[t],X2[t], ...]  +
..., 
 :
 :};
and so on.

The problem is that I have about 200 to 2000 coupled  equations
(depending upon the problem). 

The obvious attempt:

eom = {X''[t]==-0.1 X[t],
X[0]=={{0,-1},{2,.5}};
X'[t]=={{0,0},{0,0}} };
soln = NDSolve[eom,X[t],{t,0,10}];

NDSolve complains that these are not well formed  equations. 

What is the proper way to input these equations in matrix form into
NDSolve? 


-- Thanks, 
ERB


Eric R. Bittner                 bittner at uh.edu Dept. of Chemistry       
ph: 713-743-2775 University of Houston          fax: 713-743-2709
Houston TX 77204              http://k2.chem.uh.edu/bittner/
 "confutatis maledictis, flammis acribus addictis..."


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