       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,-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/