An enhanced fictitious time integration method for non-linear algebraic equations with multiple solutions: Boundary layer, boundary value and eigenvalue problems

Chein Shan Liu, Weichung Yeih, Satya N. Atluri

Research output: Contribution to journalArticle

12 Scopus citations

Abstract

When problems in engineering and science are discretized, algebraic equations appear naturally. In a recent paper by Liu and Atluri, non-linear algebraic equations (NAEs) were transformed into a nonlinear system of ODEs, which were then integrated by a method labelled as the Fictitious Time Integration Method (FTIM). In this paper, the FTIM is enhanced, by using the concept of a repellor in the theory of nonlinear dynamical systems, to situations where multiple-solutions exist. We label this enhanced method as MSFTIM. MSFTIM is applied and illustrated in this paper through solving boundary-layer problems, boundary-value problems, and eigenvalue problems with multiple solutions.

Original languageEnglish
Pages (from-to)301-323
Number of pages23
JournalCMES - Computer Modeling in Engineering and Sciences
Volume59
Issue number3
StatePublished - 2010

Keywords

  • Attracting set
  • Multiple- Solution Fictitious Time Integration Method (MSFTIM)
  • Non-linear algebraic equations
  • Ordinary differential equations
  • Repellor

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