The numerical solution of X = A₁X + XA₂ + D, X(0) = C

An improved method of solving the general matrix differential equationẊ = A₁X + XA₂ + D, X(0) = CforXis considered where A1and A2are stable matrices. The algorithm proposed requires only5n²words of memory and converges in approximately43n³ where μ is the multiplication time of the digital computer andn = max(n₁,n₂)whereA₁ ∈ R^{n₁ × n₁}, A₂ ∈ R^{n₂ × n₂}. The algorithm is extremely simple to implement.