Hillel Tal-Ezer

Spectral methods in time for hyperbolic equations

A pseudospectral numerical scheme for solving linear, periodic, hyperbolic problems is described. It has infinite accuracy both in time and in space. The high accuracy in time is achieved without increasing the computational work and memory space which is needed for a regular, one step explicit scheme. The algorithm is shown to be optimal in the sense that among all the explicit algorithms of a certain class it requires the least amount of work to achieve a certain given resolution. The class of algorithms referred to consists of all explicit schemes which may be represented as a polynomial in the spatial operator.

Spectral methods in time for parabolic problems

A pseudospectral explicit scheme for solving linear, periodic, parabolic problems is described. It has infinite accuracy both in time and in space. The high accuracy is achieved while the time resolution parameter

An accurate and efficient scheme for wave propagation in linear viscoelastic media

M(M = O({1 / {\Delta t}})

Low-order polynomial approximation of propagators for the time-dependent Schro¨dinger equation

for time marching algorithm) and the space resolution parameter

Acoustic and elastic numerical wave simulations by recursive spatial derivative operators

N(N = O({1 / {\Delta x))}}

Polynomial approximation of functions of matrices and applications

must satisfy

A pseudospectral Legendre method for hyperbolic equations with an improved stability condition

M = O(N^{1 + \varepsilon } )\varepsilon > 0

Numerical Solution of the Constant Density Acoustic Wave Equation By Implicit Spatial Derivative Operators

, compared to the common stability condition

On a fourth order accurate implicit finite difference scheme for hyperbolic conservation laws. II. Five-point schemes

M = O(N^2 )

Three dimensional wave equation depth migration by a direct solution method

, which must be satisfied in any explicit finite-order time algorithm.