TY - JOUR
T1 - The Dissipative Spectral Methods for the First Order Linear Hyperbolic Equations
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 3
SP - 493
EP - 508
PY - 2012
DA - 2012/05
SN - 5
DO - http://doi.org/10.4208/nmtma.2012.m1110
UR - https://global-sci.org/intro/article_detail/nmtma/5947.html
KW - First order hyperbolic equation, dissipative spectral method, error estimate.
AB - <p style="text-align: justify;">In this paper, we introduce the dissipative spectral methods (DSM) for the first order linear hyperbolic equations in one dimension. Specifically, we consider the Fourier DSM for periodic problems and the Legendre DSM for equations with the Dirichlet boundary condition. The error estimates of the methods are shown to be quasi-optimal for variable-coefficients equations. Numerical results are given to verify high accuracy of the DSM and to compare the proposed schemes with some high performance methods, showing some superiority in long-term integration for the periodic case and in dealing with limited smoothness near or at the boundary for the Dirichlet case.</p>