Convergence analysis of pseudo-transient continuation

C. T. Kelley*, David E. Keyes

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

209 Scopus citations


Pseudo-transient continuation (Ψtc) is a well-known and physically motivated technique for computation of steady state solutions of time-dependent partial differential equations. Standard globalization strategies such as line search or trust region methods often stagnate at local minima. Ψtc succeeds in many of these cases by taking advantage of the underlying PDE structure of the problem. Though widely employed, the convergence of Ψtc is rarely discussed. In this paper we prove convergence for a generic form of Ψtc and illustrate it with two practical strategies.

Original languageEnglish (US)
Pages (from-to)508-523
Number of pages16
JournalSIAM Journal on Numerical Analysis
Issue number2
StatePublished - 1998
Externally publishedYes


  • Global convergence
  • Nonlinear equations
  • Pseudo-transient continuation
  • Steady state solutions

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics


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