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.
Cornell University Library
arXiv.org e-Print archive
Multiscale Dynamics

Arraras, A., In't Hout, K., Hundsdorfer, W., & Portero, L. (2015). Modified Douglas Splitting Methods for Reaction-Diffusion Equations. arXiv.org e-Print archive. Cornell University Library .