Central schemes may serve as universal finite-difference methods for solving nonlinear
convection–diffusion equations in the sense that they are not tied to the specific …

We introduce new Godunov-type semidiscrete central schemes for hyperbolic systems of
conservation laws and Hamilton--Jacobi equations. The schemes are based on the use of …

We present and discuss a framework for computer-aided multiscale analysis, which enables
models at a fine (microscopic/stochastic) level of description to perform modeling tasks at a …

We construct, analyze, and implement a new nonoscillatory high-resolution scheme for two-
dimensional hyperbolic conservation laws. The scheme is a predictor-corrector method …

Kinetic equations arise in a wide variety of physical systems and efficient numerical methods
are needed for their solution. Moment methods are an important class of approximate …

Numerical simulation of high frequency acoustic, elastic or electro-magnetic wave
propagation is important in many applications. Recently the traditional techniques of ray …

We consider time-dependent (linear and nonlinear) Schrödinger equations in a
semiclassical scaling. These equations form a canonical class of (nonlinear) dispersive …

We construct quantum algorithms to compute physical observables of nonlinear PDEs with
M initial data. Based on an exact mapping between nonlinear and linear PDEs using the …

This is a summary of five lectures delivered at the CIME course on “Advanced Numerical
Approximation of Nonlinear Hyperbolic Equations” held in Cetraro, Italy, on June 1997 …

Second order accurate (first order at extrema) cell averaged based approximations
extending the Lax–Friedrichs central scheme, using component-wise rather than field-by …