@article{3cf69126cff649388830f63177e94234,
title = "On Preconditioned Iterative Methods for Burgers Equations",
abstract = "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.",
keywords = "Burgers equation, GMRES method, Preconditioners, Sinc–Galerkin discretization, Toeplitz‐like matrices",
author = "Bai, {Zhong Zhi} and Huang, {Yu Mei} and Ng, {Michael K.}",
note = "Funding information: State Key Laboratory of Scientific/Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100080, The People{\textquoteright}s Republic of China (
[email protected]). This author{\textquoteright}s research was supported by The National Basic Research Program (2005CB321702), The China NNSF National Outstanding Young Scientist Foundation (10525102), and The National Natural Science Foundation (10471146), The People{\textquoteright}s Republic of China. Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong (
[email protected],
[email protected]). The research of the third author was supported in part by RGC grants 7046/03P, 7035/04P, and 7035/05P, and HKBU FRGs. Publisher copyright: Copyright {\textcopyright} 2007 Society for Industrial and Applied Mathematics",
year = "2007",
month = feb,
day = "15",
doi = "10.1137/060649124",
language = "English",
volume = "29",
pages = "415--439",
journal = "SIAM Journal on Scientific Computing",
issn = "1064-8275",
publisher = "Society for Industrial and Applied Mathematics (SIAM)",
number = "1",
}