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Matrix differential equation in NDSolve

• To: mathgroup at smc.vnet.net
• Subject: [mg63298] Matrix differential equation in NDSolve
• From: Maarten <maarten at stack.nl>
• Date: Fri, 23 Dec 2005 05:08:24 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

Hello,

I would like to evaluate a matrix equation of the form:

S'[t]==A(x).S[t]+B(x)
x'[t]==f[x]

in NDSolve where A and B are symbolic matrices. The problem is that S[t] is an unknown n x m matrix, of the same dimension as B. If I enter the first equation as shown above, Mathematica evaluates it to

{A(x).S[t]+B(x){1,:},A(x).S[t]+B(x){2,:},...,A(x).S[t]+B(x){m,:}}

that is, it assumes S[t] is a vector which is replicated to match the dimensions of B(x). How can I get Mathematica to respect the fact that S[t] is of dimension B in NDSolve. I tried holdform but this does not evaluate in NDSolve