Stability of ADI schemes applied to convection-diffusion equations with mixed derivative terms

TitleStability of ADI schemes applied to convection-diffusion equations with mixed derivative terms
Publication TypeJournal Article
Year of Publication2007
Authorsin't Hout KJ, Welfert BD
JournalApplied Numerical Mathematics
Volume57
Pagination19–35
Abstract

We consider Alternating Direction Implicit (ADI) schemes for the numerical solution of initial-boundary value problems for convection–diffusion equations with cross derivative terms. We derive new linear stability results for three ADI schemes that have previously been studied in the literature. These results are subsequently used to show that the ADI schemes under consideration are unconditionally stable when applied to finite difference discretizations of general parabolic two-dimensional convection–diffusion equations. Supporting numerical evidence is included.