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Linear Differential Equations with Matrices

• To: mathgroup at smc.vnet.net
• Subject: [mg59413] Linear Differential Equations with Matrices
• From: David Boily <dsboily at fastmail.ca>
• Date: Tue, 9 Aug 2005 03:30:44 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

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

• Follow-Ups:
  • Re: Linear Differential Equations with Matrices
    • From: Selwyn Hollis <sh2.7183@earthlink.net>