Efficient matrix-valued algorithms for solving stiff Riccati differential equations

Efficient algorithms are developed for solving time-varying stiff Riccati differential equations (RDEs). The method is also applicable to time-invariant, nonstiff problems. The algorithm can handle various classes of RDEs, i.e., time-varying or time-invariant, symmetric or nonsymmetric, and rectangular or square. The amount of work required to compute the solution per time step is O(n³) FLOPS, whereas other widely used methods for stiff equations, such as direct integration by using implicit multistep methods, require O (n⁶) FLOPS in the time-varying case. Numerical experiments have confirmed that the method is promising for the numerical solution of stiff RDEs