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Continuation Methods for Nonlinear Eigenvalue Problems via a Sinc-Galerkin Scheme

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Computation and Control III

Part of the book series: Progress in Systems and Control Theory ((PSCT,volume 15))

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Abstract

In this paper we will be looking at semilinear boundary value problems of the form

$$ \begin{gathered} \mathcal{L}u(x)\bar = u^{''} (x) + cu(x) = f(x,u(x),\lambda ),a < x < b \hfill \\ u(a) = u(b) = 0, \hfill \\ \end{gathered} $$
(1.1)

where c is a fixed constant and A is a parameter. Here, a and b need not be finite. This type of problem often arises as the equilibrium problem for a scalar evolution equation. The purpose of this paper is to illustrate the use of the Sinc-Galerkin method for one-parameter problems such as (1.1).

Supported in part by NSF grant DMS-9113526.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Montana State University, Bozeman, Montana, 59717, USA

    Jack D. Dockery & Nancy J. Lybeck

Authors
  1. Jack D. Dockery
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  2. Nancy J. Lybeck
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Editors and Affiliations

  1. Department of Mathematics, Montana State University, Bozeman, Montana, 59717, USA

    Kenneth Bowers  & John Lund  & 

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© 1993 Springer Science+Business Media New York

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Dockery, J.D., Lybeck, N.J. (1993). Continuation Methods for Nonlinear Eigenvalue Problems via a Sinc-Galerkin Scheme. In: Bowers, K., Lund, J. (eds) Computation and Control III. Progress in Systems and Control Theory, vol 15. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0321-6_11

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  • DOI: https://doi.org/10.1007/978-1-4612-0321-6_11

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6706-5

  • Online ISBN: 978-1-4612-0321-6

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