Approximate solution of hyperbolic conservation laws by discrete mollification

We consider explicit schemes for the numerical solution of one dimensional linear and nonlinear hyperbolic conservation laws. We show that the combination of these methods with discrete mollification, yields new methods with the following characteristics: Larger time steps are allowed and stability is preserved. Furthermore, they can be implemented in such a way that nonoscillatory solutions are obtained. We include theoretical results and a well selected set of encouraging numerical experiments.