  Many interesting applications of hyperbolic systems of equations are stiff,
and require the time step to satisfy restrictive stability conditions. One way
to avoid small time steps is to use implicit time integration. Implicit
integration is quite straightforward for first order schemes. High order
schemes instead need also to control spurious oscillations, which requires
limiting in space and time also in the implicit case. We propose a framework to
simplify considerably the application of high order non oscillatory schemes
through the introduction of a low order implicit predictor, which is used both
to set up the nonlinear weights of a standard high order space reconstruction,
and to achieve limiting in time. In this preliminary work, we concentrate on
the case of a third order scheme, based on DIRK integration in time and CWENO
reconstruction in space. The numerical tests involve linear and nonlinear
scalar conservation laws.
