Matrix differential equation

*To*: mathgroup at smc.vnet.net*Subject*: [mg50848] Matrix differential equation*From*: "Marco Malvaldi" <M.Malvaldi at chem.rug.nl>*Date*: Thu, 23 Sep 2004 06:48:07 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

It is possible to numerically solve a general matrix differential equation with Mathematica? From the example in Mathematica 5 tutorial, I found that this problem can be solved: k = 10 A = -{{1, 2, 3}, {4, 5 , 6}, {7, 8 , 9}}; K = -{{0, k, 0}, {0, 0 , 0}, {0, 0 , 0}}; X0 = {{1, 0, 0}, {0, 1 , 0}, {0, 0 , 1}}; KT = Transpose[K] matrixExpA = X /. First[ NDSolve[X'[t] == 0.5*IdentityMatrix[3] .(X[t]) + K.X[t] + X[t].KT && X[0] == IdentityMatrix[3], X, {t, 0, 10}]] Anyway, when I try to submit this problem: matrixExpA = X /. First[ NDSolve[X'[t] == 0.5*IdentityMatrix[3] +(X[t]) + K.X[t] + X[t].KT && X[0] == IdentityMatrix[3], X, {t, 0, 10}]] the answer is: NDSolve::ndfdmc: Computed derivatives do not have dimensionality consistent with the initial conditions. even if what I'm doing is to sum a 3x3 matrix to a system of 3X3 matrix. Regards Marco Malvaldi