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Re: Re: Linear Differential Equations with Matrices

• To: mathgroup at smc.vnet.net
• Subject: [mg59622] Re: [mg59461] Re: [mg59413] Linear Differential Equations with Matrices
• From: Chris Chiasson <chris.chiasson at gmail.com>
• Date: Sun, 14 Aug 2005 04:38:08 -0400 (EDT)
• References: <200508090730.DAA19044@smc.vnet.net> <200508100656.CAA04520@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

an shorter way to specify the elements of the P matrix:
P[t]=Array[p[##][t]&,{3,3}]

(if you are willing to refer to your functions as p[1,1][t],
p[1,2][t], etc -- otherwise you could combine the above approach with
ToString and ToExpression)

On 8/10/05, Selwyn Hollis <sh2.7183 at earthlink.net> wrote:
> 
> On Aug 9, 2005, at 3:30 AM, David Boily wrote:
> 
> > How can I solve this system with mathematica:
> >
> > <<LinearAlgebra`MatrixManipulation`
> >
> > A = {{-F1, 0, 0}, {0, -F2, 0}, {1, -1, 0}}
> > Q = {{0, 0, 0}, {0, 0, 0}, {0, 0, 1}}
> > Z = ZeroMatrix[3]
> >
> > DSolve[{P'[t] + Transpose[A].P[t] + P[t].A + Q == Z, R'[t] +
> > Transpose[A].R[t] + P[t] == Z, P[T]==Z, R[T]==Z}, {P, R}, t]
> >
> > where P and R are 3x3 matrix functions of t. Mathematica tells me:
> >
> > Solve::eqf: {{-F1, 0, 1}, <<2>>} . R[t] + <<2>> == {{0, <<2>>}, <<2>>}
> >      is not a well-formed equation.
> >
> > shouldn't this be possible without going the long way and defining
> >
> > P[t_]:={{p11[t], p12[t], p13[t]}, {p21[t], p22[t], p23[t]}, {p31
> > [t],p32[t], p33[t]}}
> > R[t_]:={{r11[t], r12[t], r13[t]}, {r21[t], r22[t], r23[t]}, {r31
> > [t],r32[t], r33[t]}}
> >
> > Thanks,
> >
> > David Boily
> > Centre for Intelligent Machines
> > McGill University
> > Montreal, Quebec
> >
> 
> 
> It would be nice, but unless I'm mistaken the only way to do it is to
> provide DSolve with a flat list of scalar equations. Anyhow, the
> following does the trick:
> 
> << "LinearAlgebra`MatrixManipulation`"
> A = {{-F1, 0, 0}, {0, -F2, 0}, {1, -1, 0}};
> Q = {{0, 0, 0}, {0, 0, 0}, {0, 0, 1}};
> Z = ZeroMatrix[3];
> 
> P[t_] := {{p11[t], p12[t], p13[t]}, {p21[t], p22[t], p23[t]}, {p31
> [t], p32[t], p33[t]}}
> R[t_] := {{r11[t], r12[t], r13[t]}, {r21[t], r22[t], r23[t]}, {r31
> [t], r32[t], r33[t]}}
> 
> deqns = Flatten[ Thread /@ Flatten[ Thread /@
>         {P'[t] + Transpose[A].P[t] + P[t].A + Q == Z,
>          R'[t] + Transpose[A].R[t] + P[t] == Z,
>          P[T] == Z, R[T] == Z} ] ];
> 
> vars = Flatten[{P[t], R[t]}];
> 
> solnrules = DSolve[deqns, vars, t]//First//Simplify
> 
> MatrixForm[ Psoln = P[t] /. solnrules ]
> 
> MatrixForm[ Rsoln = R[t] /. solnrules ]
> 
> 
> ----------------------
> Selwyn Hollis
> http://www.appliedsymbols.com
> 
> 


-- 
Chris Chiasson
http://chrischiasson.com/
1 (810) 265-3161

• References:
  • Linear Differential Equations with Matrices
    • From: David Boily <dsboily@fastmail.ca>
  • Re: Linear Differential Equations with Matrices
    • From: Selwyn Hollis <sh2.7183@earthlink.net>