What is dual time stepping? Also, what is preconditioning?

I'm a bit confused by the phrase and the nearby threads on this same topic. There is a thing called pseudo time stepping that may also be frequently referred to as dual time stepping. As I recall, it is discussed at length in the latest edition of

http://www.amazon.com/exec/obidos/tg...glance&s=books

along with the preconditioning that is involved.

There is a different concept that also goes by the name dual time stepping. Imagine you are solving a convection-diffusion problem. Imagine the stability restricted time step of the diffusion term was much more severe than the convection term. Imagine running two different explicit time integration methods to solve this problem where the time steps for each method were different. The integrator acting on the diffusion term will be busily at work while the other integrator sit by doing nothing most of the time. This can also be called subcycling or, maybe best, a partitioned multirate method. The problems with these methods are many. Beyond getting the elemental methods right, there is coupling accuracy/error and coupling stability. Without a strong theoretical basis to give one the order conditions and the stability function, designing these is a shot in the dark.

http://scholar.google.com/scholar?hl...&q=partitioned+multirate+RUNGE%E2%80%93KUTTA&btnG=Search

Hi Runge_Kutta,

Thank you, that makes more sense. Do you have any idea what pseudo- time stepping is? Any information on this or preconditioning would be helpful. I want to know purely for interest sake, I have no need to work with these techniques. I don't have access to the Tannehill book.