Abstract: Based on the corresponding relation between LQ control and computational structural mechanics, the interval mixed energy matrices Q2,G2 and Φ2 are put forward in this paper. Then, the formulas for the condensation algorithm of the LQ control problem are derived. From the condensation formulas, the differential equations for these matrices are introduced. The Riccati equation is one of them. These equations are solved by the series expansion method when △t is very small. Using the higher approximation of the very small interval, △t, one can speed up the iterative solution of the algebraic Riccati equation.