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Equations with infinite delay: Numerical bifurcation analysis via pseudospectral discretization

Author

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  • Gyllenberg, Mats
  • Scarabel, Francesca
  • Vermiglio, Rossana

Abstract

We address the problem of the numerical bifurcation analysis of general nonlinear delay equations, including integral and integro-differential equations, for which no software is currently available. Pseudospectral discretization is applied to the abstract reformulation of equations with infinite delay to obtain a finite dimensional system of ordinary differential equations, whose properties can be numerically studied with well-developed software. We explore the applicability of the method on some test problems and provide some numerical evidence of the convergence of the approximations.

Suggested Citation

  • Gyllenberg, Mats & Scarabel, Francesca & Vermiglio, Rossana, 2018. "Equations with infinite delay: Numerical bifurcation analysis via pseudospectral discretization," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 490-505.
    • Handle: RePEc:eee:apmaco:v:333:y:2018:i:c:p:490-505
    DOI: 10.1016/j.amc.2018.03.104
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