Chebyshev pseudospectral method for wave equation with absorbing boundary conditions that does not use a first order hyperbolic system

Authors:
F. S. V. Bazán
Affiliations:
Department of Mathematics, Federal University of Santa Catarina, 88040-900 - Florianópolis SC, Brazil
Venue:
Mathematics and Computers in Simulation
Year:
2010

Citing 10
Cited 0

Absorbing boundaries for wave propagation problems

Journal of Computational Physics
A modified Chebyshev pseudospectral method with an O(N–1) time step restriction

Journal of Computational Physics
A pseudospectral Chebychev method for the 2D wave equation with domain stretching and absorbing boundary conditions

Journal of Computational Physics
Pseudospectra for the wave equation with an absorbing boundary

Journal of Computational and Applied Mathematics
Matrix computations (3rd ed.)

Matrix computations (3rd ed.)
Stability of a Chebychev pseudospectral solution of the wave equation with absorbing boundaries

Journal of Computational and Applied Mathematics
Implementation of Diagonally Implicit Multistage Integration Methods for Ordinary Differential Equations

SIAM Journal on Numerical Analysis
Diagonally implicit multistage integration methods for pseudospectral solutions of the wave equation

Applied Numerical Mathematics - Auckl numerical ordinary differential equations (ANODE 98 workshop)
Spectral methods in MATLAB

Spectral methods in MATLAB
A note on stability of pseudospectral methods for wave propagation

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

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 Chebyshev pseudospectral collocation method coupled with integration in time by the Runge-Kutta method. Stability limits on the timestep for arbitrary speed are calculated and verified numerically. Furthermore, theoretical properties of two methods by Jackiewicz and Renaut are derived, including, in particular, a result that corrects some conclusions of these authors. Numerical results that verify the theory and illustrate the effectiveness of the proposed approach are reported.