We have studied the t-system by applying it to different ODEs and investigating its performance and also carrying out some theoretical analysis.
One focus of our work is applying the t-system to very simple systems. The idea being that some theoretical results can be obtained for these problems, where they could not be in more complex or general problems.
We have applied Chorin's t-system to the Fourier transform of the PDE u_t = sin(x)u_x. At least for small t, we have found significant improvement in accuracy over a simple Galerkin truncation.
We have also applied the t-system to some equations that come from particle-method discretization of PDEs and obtained interesting results.
This is joint work with Alina Chertock and David Gottlieb.