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

An improved method of solving 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
5n^{2}
words of memory and converges in approximately
43n^{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 extremely simple to implement.