A second-order stabilization method for linearizing and decoupling nonlinear parabolic systems

BUYANG LI, YUKI UEDA, GUANYU ZHOU

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)2736-2763
Number of pages28
JournalSIAM Journal on Numerical Analysis
Volume58
Issue number5
DOIs
Publication statusPublished - 2020

Keywords

  • Convergence
  • Decoupling
  • Linearization
  • Nonlinear parabolic system
  • Stabilization

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

Fingerprint Dive into the research topics of 'A second-order stabilization method for linearizing and decoupling nonlinear parabolic systems'. Together they form a unique fingerprint.

Cite this