An Approximate Newton Method for Coupled Nonlinear Systems.

Abstract

The author proposes an approximate Newton method for solving a coupled nonlinear system. The method involves applying the basic iteration S of a general solver for the equation G(u,t)=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. The author derives conditions for S under which the method is locally convergent. Basically, if S is sufficiently contractive for G, then convergence for the coupled system is guaranteed. Otherwise, it shown how to construct a S from S for which convergence is assured. These results are applied to continuation methods where N represents a pseudo-arclength condition. He show that under certain conditions the algorithm converges if S is convergent for G. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1984
Accession Number
ADA139589

Entities

People

  • T. F. Chan

Organizations

  • Yale University

Tags

Communities of Interest

  • Advanced Electronics

DTIC Thesaurus Topics

  • Algorithms
  • Applied Mathematics
  • Classification
  • Computational Science
  • Differential Equations
  • Efficiency
  • Eigenvalues
  • Elimination
  • Equations
  • Iterations
  • Linear Systems
  • Mathematics
  • Navier Stokes Equations
  • Nonlinear Systems
  • Optimization
  • Partial Differential Equations
  • Security

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)