The time-dependent incompressible Navier-Stokes system of equations contains both parabolic and elliptic features. The stability of this mixed system does not follow directly from the stability theory for standard parabolic systems because of the interplay between the elliptic and parabolic features.

In this talk I will discuss a definition of stability for multi-step schemes applied to the time-dependent Stokes equations. This definition allows for the proof of stability for certain high-order accurate schemes for the time-dependent incompressible Stokes equations.

This work is joint with Prof. Young Lee of Manchester College, North Manchester, IN, USA.

MINISIMPOSIUM SESSION: 16. Stability Issues for IVP methods