Differential eigenvalue problems in which the parameter appears nonlinearly

T. J. Bridges, P. J. Morris

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196 Scopus citations


Several methods are examined for determining the eigenvalues of a system of equations in which the parameter appears nonlinearly. The equations are the result of the discretization of differential eigenvalue problems using a finite Chebyshev series. Two global methods are considered which determine the spectrum of eigenvalues without an initial estimate. A local iteration scheme with cubic convergence is presented. Calculations are performed for a model second order differential problem and the Orr-Sommerfeld problem for plane Poiseuille flow.

Original languageEnglish (US)
Pages (from-to)437-460
Number of pages24
JournalJournal of Computational Physics
Issue number3
StatePublished - Sep 1984

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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