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The Dissipative Spectral Methods for the First Order Linear Hyperbolic Equations

Published online by Cambridge University Press:  28 May 2015

Lian Chen ,
Zhongqiang Zhang  and
Heping Ma
Lian Chen*
Affiliation:
Department of Mathematics, College of Sciences, Shanghai University, Shanghai, 200444, China
Zhongqiang Zhang*
Affiliation:
Division of Applied Mathematics, Brown University, Providence, Rhode Island, 02912, USA
Heping Ma*
Affiliation:
Department of Mathematics, College of Sciences, Shanghai University, Shanghai, 200444, China
*
Corresponding author.Email address:[email protected]
Corresponding author.Email address:[email protected]
Corresponding author.Email address:[email protected]
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Abstract

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.

Keywords

65N1565N35First order hyperbolic equationdissipative spectral methoderror estimate
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 5 , Issue 3 , August 2012 , pp. 493 - 508
Copyright
Copyright © Global Science Press Limited 2012

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