Spatial discretization of some partial differential equations (PDEs) gives rise to stiff systems of ordinary differential equations (ODEs). This is the case, for example, for equations of motion associated with the semi-convection problem in the simulation of stellar convection, and for some other models of flow with diffusion that appear in astrophysics. To solve the system of ODEs, IMplicit-EXplicit (IMEX) time stepping methods, specially constructed to have different stability properties, are used. Ongoing work continues with the study of some implementation issues.