Numerische Mathematik

, Volume 91, Issue 4, pp 627–648

Stability of piecewise polynomial collocation for computing periodic solutions of delay differential equations

  • K. Engelborghs
  • E.J. Doedel
Original article

Summary.

We prove numerical stability of a class of piecewise polynomial collocation methods on nonuniform meshes for computing asymptotically stable and unstable periodic solutions of the linear delay differential equation \(\dot y(t) = a(t)y(t)+b(t)y(t-\tau) + f(t)\) by a (periodic) boundary value approach. This equation arises, e.g., in the study of the numerical stability of collocation methods for computing periodic solutions of nonlinear delay equations. We obtain convergence results for the standard collocation algorithm and for two variants. In particular, estimates of the difference between the collocation solution and the true solution are derived. For the standard collocation scheme the convergence results are “unconditional”, that is, they do not require mesh-ratio restrictions. Numerical results that support the theoretical findings are also given.

Mathematics Subject Classification (1991): 65L60 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • K. Engelborghs
    • 1
  • E.J. Doedel
    • 2
  1. 1.University of Leuven, Department of Computer Science, Celestijnenlaan 200 A, 3001 Heverlee, Belgium; e-mail: koen.engelborghs@cs.kuleuven.ac.be BE
  2. 2.Applied and Computational Mathematics, California Institute of Technology, Pasadena CA 91125, USA US

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