In 1945, W. Taylor discovered the barycentric formula for evaluating the interpolating
polynomial. In 1984, W. Werner has given first consequences of the fact that the formula …

We describe a new scheme for evolving the equations of force-free electrodynamics, the
vanishing-inertia limit of magnetohydrodynamics. This pseudo-spectral code uses global …

Gauss and Clenshaw–Curtis quadrature, like Legendre and Chebyshev spectral methods,
make use of grids strongly clustered at boundaries. From the viewpoint of polynomial …

It is well known that high-order finite-difference methods may become unstable due to the
presence of boundaries and the imposition of boundary conditions. For uniform grids …

Prolate spheroidal functions of order zero are generalizations of Legendre polynomials
which, when the “bandwidth parameter” c> 0, oscillate more uniformly on x∈[− 1, 1] than …

Differentiation matrices obtained with infinitely smooth radial basis function (RBF)
collocation methods have, under many conditions, eigenvalues with positive real part …

Spectral-element methods, based on high-order polynomials, are among the most
commonly used techniques for computing accurate simulations of wave propagation …

We examine the merits of using prolate spheroidal wave functions (PSWFs) as basis
functions when solving hyperbolic PDEs using pseudospectral methods. The relevant …

In this article we present the essential aspects of spectral methods and their applications to
the numerical solution of Partial Differential Equations. Starting from the fundamental ideas …

The Chebyshev pseudospectral semi-discretization preconditioned by a transformation in
space is applied to delay partial differential equations. The Jacobi waveform relaxation …