The numerical solution ofX = A_{1}X + XA_{2} + D, X(0) = C

The numerical solution of the general matrix differential equation
\dot{X} = A_{1}X + XA_{2} + D, X(0) = C
for
X
is considered where A
1
and A
2
are stable matrices. The algorithm proposed requires only
8n^{2}
words of memory (for large
n
) and converges in approximately
50n^{3} \mu
s where μ is the multiplication time of the digital computer, and
n = \max(n_{1},n_{2})
where
A_{1} \in R^{n_{1} \times n_{1}} , A_{2} \in R^{n_{2} \times n_{2}}
. The algorithm is particularly suitable for systems where
n
is large (e.g,
n \gg 10
).