A Pseudo-Arclength Continuation Method for Nonlinear Eigenvalue Problems.

Abstract

A variant of the classical pseudo-arclength continuation method is proposed. Basically, the method can be viewed as pseudo-arclength continuation in (r, lambda) space where r is a functional of the solution. Another difference is a three-parameter predictor instead of the standard Euler step. This predictor, as well as the Newton corrector iteration, are justified and some numerical results for reaction-diffusion equations are presented. The method provides a simple algebraic check for symmetry breaking bifurcation, the most common type of secondary bifurcation in physical examples. Keywords: parameter dependent boundary value problems; continuation algorithm; singular points; symmetry breaking bifurcation; reaction diffusion equations.

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1985
Accession Number
ADA173019

Entities

People

  • Hans D. Mittelmann

Organizations

  • Arizona State University

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Banach Space
  • Bessel Functions
  • Boundaries
  • Boundary Value Problems
  • Computations
  • Convex Sets
  • Differential Equations
  • Eigenvalues
  • Equations
  • Formulas (Mathematics)
  • Hilbert Space
  • Integral Equations
  • Partial Differential Equations
  • Polynomials
  • Riccati Equation
  • Variational Principles

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Parallel and Distributed Computing.

Technology Areas

  • Space
  • Space - Spacecraft Maneuvers