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..."