Critical lengths by numerical integration of the associated Riccati equation to singularity

摘要

Bounds are obtained for the critical length (escape time) associated with a solution of a matrix Riccati equation. The bounds are computationally practical in the sense that the quantities appearing can be computed in terms of a known value of the solution at any point. It is suggested that these bounds will frequently allow practical estimation of the accuracy in determining a critical length by integrating the Riccati equation to “blowup”. Practical aspects of such an application are discussed, and two examples are given.