On Preconditioned Iterative Methods for Burgers Equations

Zhong Zhi Bai, Yu Mei Huang, Michael K. Ng

Research output: Contribution to journalJournal articlepeer-review

47 Citations (Scopus)
19 Downloads (Pure)


We study the Newton method and a fixed‐point method for solving the system of nonlinear equations arising from the Sinc–Galerkin discretization of the Burgers equations. In each step of the Newton method or the fixed‐point method, a structured subsystem of linear equations is obtained and needs to be solved numerically. In this paper, preconditioning techniques are applied to solve such linear subsystems. The bounds for eigenvalues of the preconditioned matrices are derived and numerical examples are given to illustrate the effectiveness of the proposed methods. We also find that a combination of the Newton/fixed‐point iteration with the preconditioned GMRES method is quite efficient for the Sinc–Galerkin discretization of the Burgers equations.

Original languageEnglish
Pages (from-to)415-439
Number of pages25
JournalSIAM Journal on Scientific Computing
Issue number1
Publication statusPublished - 15 Feb 2007

Scopus Subject Areas

  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Burgers equation
  • GMRES method
  • Preconditioners
  • Sinc–Galerkin discretization
  • Toeplitz‐like matrices


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