  A method is presented for obtaining rigorous error estimates for approximate
solutions of the Riccati equation, with real or complex potentials. Our main
tool is to derive invariant region estimates for complex solutions of the
Riccati equation. We explain the general strategy for applying these estimates
and illustrate the method in typical examples, where the approximate solutions
are obtained by glueing together WKB and Airy solutions of corresponding
one-dimensional Schrodinger equations. Our method is motivated by and has
applications to the analysis of linear wave equations in the geometry of a
rotating black hole.
