Rational approximate solutions and error bounds for the nonsymmetric Riccati matrix differential equation (Q1194392)

Consider the \(n \times n\) matrix Riccati differential equation \(W'(t)=C - DW(t)-W(t)A - W(t)BW(t)\), \(W(0) = W_ 0\), with constant matrix coefficients. First the interval is estimated where the exact solution is defined. Then the error of the approximate solution \(W_ q(t)\) is estimated, where \(W_ q(t)\) is obtained replacing the matrix exponential \(e^{St}\) of \(S=\bigl[{A\atop C}{B\atop -D}\bigr]\) by \(I_{2n} + St + \dots + (St)^ q/q!\).