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Shooting methods for a PT-symmetric periodic eigenvalue problem

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Abstract

We present a rigorous analysis of the performance of some one-step discretization schemes for a class of PT-symmetric singular boundary eigenvalue problem which encompasses a number of different problems whose investigation has been inspired by the 2003 article of Benilov et al. (J Fluid Mech 497:201–224, 2003). These discretization schemes are analyzed as initial value problems rather than as discrete boundary problems, since this is the setting which ties in most naturally with the formulation of the problem which one is forced to adopt due to the presence of an interior singularity. We also devise and analyze a variable step scheme for dealing with the singular points. Numerical results show better agreement between our results and those obtained from small-ϵ asymptotics than has been shown in results presented hitherto.

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Authors and Affiliations

  1. Dipartimento di Matematica Applicata “U.Dini”, Università di Pisa, Pisa, Italy

    Lidia Aceto & Cecilia Magherini

  2. School of Mathematics, Cardiff University, Cardiff, CF24 4AG, UK

    Marco Marletta

Authors
  1. Lidia Aceto
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  2. Cecilia Magherini
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  3. Marco Marletta
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Correspondence to Lidia Aceto.

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Aceto, L., Magherini, C. & Marletta, M. Shooting methods for a PT-symmetric periodic eigenvalue problem. Numer Algor 57, 513–536 (2011). https://doi.org/10.1007/s11075-010-9443-4

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  • DOI: https://doi.org/10.1007/s11075-010-9443-4

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