  We present modifications of the second-order Douglas stabilizing corrections
method, which is a splitting method based on the implicit trapezoidal rule.
Inclusion of an explicit term in a forward Euler way is straightforward, but
this will lower the order of convergence. In the modifications considered here,
explicit terms are included in a second-order fashion. For these modified
methods, results on linear stability and convergence are derived. Stability
holds for important classes of reaction-diffusion equations, and for such
problems the modified Douglas methods are seen to be often more efficient than
related methods from the literature.
