Matrix differential equation using matlab

[quansnow]

For d X/d t=AX + XB+ C, where A, B, and C are the given 6*6 matrices,

I use the following way to solve it,

let X= X11 X12 X13 X14 X15 X16
X21 X22 X23 X24 X25 X26
X31 X32 X33 X34 X35 X36
X41 X42 X43 X44 X45 X46
X51 X52 X53 X54 X55 X56
X61 X62 X63 X64 X65 X66
then plug X into d X/d t=AX + XB+ C to get 36 equations as follows
d X11/d t=...;
d X12/d t=...;
d X13/d t=...;
......;
then solve these 36 equations by using mathlab command ode45.

The method I use is cumbersome.

Is there any easy way to solve d X/d t=AX + XB+ C?

Thanks!

 

[NateD]

Yes, there is an easier way to solve this equation. You can use the matrix exponential approach to solve this equation. This involves solving the following equation: X(t) = exp(At)X(0) + ∫exp(A(t-τ))Cdτ. This equation can be solved using numerical integration techniques.