Newton method for nonlinear dynamic systems with adaptive time stepping

Wensheng Shen, Changjiang Zhang, Jun Zhang, Xiaoqian Ma

Research output: Contribution to journalArticlepeer-review


This paper presents a nonlinear solver based on the Newton-Krylov methods, where the Newton equations are solved by Krylov-subspace type approaches. We focus on the solution of unsteady systems, in which the temporal terms are discretized by the backward Euler method using finite difference. To save computational cost, an adaptive time stepping is used to minimize the number of time steps. The developed program can be applied to solve any nonlinear equations, provided the users could supply the discrete form of the equations. In particular, the nonlinear solver is implemented to solve unsteady reacting flows.

Original languageEnglish
Pages (from-to)891-902
Number of pages12
JournalJournal of Universal Computer Science
Issue number6
StatePublished - 2010


  • Diffusion flame
  • Iterative solver
  • Newton-krylov method
  • Nonlinear dynamics

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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