@article{066c232f7b18409f9b2a6538dc8315fe,
title = "A second-order stabilization method for linearizing and decoupling nonlinear parabolic systems",
abstract = "A new time discretization method for strongly nonlinear parabolic systems is constructed by combining the fully explicit two-step backward difference formula and a second-order stabilization of wave type. The proposed method linearizes and decouples a nonlinear parabolic system at every time level, with second-order consistency error. The convergence of the proposed method is proved by combining energy estimates for evolution equations of parabolic and wave types with the generating function technique that is popular in studying ordinary differential equations. Several numerical examples are provided to support the theoretical result.",
keywords = "Convergence, Decoupling, Linearization, Nonlinear parabolic system, Stabilization",
author = "BUYANG LI and YUKI UEDA and GUANYU ZHOU",
note = "Funding Information: \ast Received by the editors October 28, 2019; accepted for publication (in revised form) July 17, 2020; published electronically September 30, 2020. https://doi.org/10.1137/19M1296136 \bfF \bfu \bfn \bfd \bfi \bfn \bfg : The work of the first author was partially supported by Hong Kong Polytechnic University project ZZKQ. The work of the second author was partially supported by Hong Kong RGC grant 15300817. \dagger Department of Applied Mathematics, Hong Kong Polytechnic University, Hung Hom, Hong Kong (buyang.li@polyu.edu.hk). \ddagger Department of Applied Mathematics, Hong Kong Polytechnic University, Hung Hom, Hong Kong. Current address: Waseda Research Institute for Science and Engineering, Faculty of Science and Engineering, Waseda University, Tokyo, Japan (yuki.ueda@aoni.waseda.jp). \S Corresponding author. Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, No. 4, Section 2, North Jianshe Road, Chengdu, China (zhoug@uestc.edu.cn, wind geno@live.com). Publisher Copyright: {\textcopyright} 2020 Society for Industrial and Applied Mathematics ",
year = "2020",
doi = "10.1137/19M1296136",
language = "English",
volume = "58",
pages = "2736--2763",
journal = "SIAM Journal on Numerical Analysis",
issn = "0036-1429",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "5",
}