Approximate solution of hyperbolic conservation laws by discrete mollification (Q1030790)

The authors propose explicit schemes for one-dimensional linear and nonlinear hyperbolic conservation laws. Combination of these methods with discrete mollification yields new methods with the following properties: Large time steps are allowed and stability is preserved. The implementation can be done in such way that nonoscillatory mollification solutions are obtained. There is a number of numerical experiments which illustrate the theory.