APPROXIMATE NEWTON METHOD FOR COUPLED NONLINEAR SYSTEMS.

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Abstract

We propose an approximate Newton method for solving the coupled nonlinear system G(u, t) equals 0 and N(u, t) equals 0. The method involves applying the basic iteration S of a general solver for the equation G(u, t) equals 0, with t fixed. It is therefore well suited for problems for which such a solver already exists or can be implemented more efficiently than a solver for the coupled system. We derive conditions for S under which the method is locally convergent. The results are applied to continuation methods where N represents a pseudo-arclength condition. We show that under certain conditions the algorithm converges if S is convergent for G. Numerical results are given for a two-level nonlinear multi-grid solver applied to a nonlinear elliptic problem.
Original languageEnglish
Pages (from-to)904-913
Number of pages10
JournalSIAM Journal on Numerical Analysis
Volume22
Issue number2
DOIs
StatePublished - 1985
Externally publishedYes

Keywords

  • APPROXIMATE NEWTON METHOD
  • CONTINUATION METHODS
  • CONVERGENCE
  • COUPLED NONLINEAR SYSTEMS, MATHEMATICAL TECHNIQUES

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