  This paper deals with the numerical solution of conservation laws in the two
dimensional case using a novel compact implicit time discretization that enable
applications of fast algebraic solvers. We present details for the second order
accurate parametric scheme based on the finite volume method including simple
variants of ENO (Essentially Non-Oscillatory) and WENO (Weighted Essentially
Non-Oscillatory) approximations. We present numerical experiments for
representative linear and nonlinear problems.
