In this talk, we discuss a numerical scheme for the accurate and efficient solution of time dependent partial differential equations. The technique first discretizes the temporal direction using Gaussian type nodes and spectral integration, and applies low-order time marching schemes to form a preconditioned elliptic system. The better conditioned system is then solved iteratively using Jacobi-Free Newton–Krylov techniques, and each function evaluation is simply one low-order time-stepping approximation of the error by solving a decoupled system using available fast elliptic equation solvers. Preliminary numerical experiments show that this technique can be unconditionally stable and spectrally accurate in both temporal and spatial directions.