We examine to what extent finite-dimensional spaces defined on locally compact subsets of the line and possessing various weak Chebyshev properties (involving sign changes, zeros, alternation of best approximations, and peak points) can be uniformly approximated by a sequence of spaces having related properties. r 2003 Elsevier Science (USA). All rights reserved.

A method for computing highly accurate numerical solutions of 1D convection–diffusion equations is proposed. In this method, the equation is first discretized with respect to the spatial variable, transforming the original problem into a set of ordinary differential equations, and then the resulting system is integrated in time by the fourth-order Runge–Kutta method. Spatial discretization is d...

The analysis and solution of wave equations with absorbing boundary conditions by using a related first order hyperbolic system has become increasingly popular in recent years. At variance with several methods which rely on this transformation, we propose an alternative method in which such hyperbolic system is not used. The method consists of approximation of spatial derivatives by the Chebysh...

Calculating the spectral function of two dimensional systems is arguably one most pressing challenges in modern computational condensed matter physics. While efficient techniques are available lower dimensions, present insurmountable hurdles, ranging from sign problem quantum Monte Carlo (MC), to entanglement area law tensor network based methods. We hereby a variational approach on Chebyshev e...

Sand waves form a prominent regular pattern in the offshore seabeds of sandy shallow seas and pose a threat to a range of offshore activities. A two-dimensional vertical (2DV) flow and morphological simulation model describing the behaviour of these sand waves has been developed. The simulation model contains the 2DV shallow water equations, with a free water surface and a general bed load form...