Equations with infinite delay: Numerical bifurcation analysis via pseudospectral discretization

Mats Gyllenberg, Francesca Scarabel and Rossana Vermiglio

Applied Mathematics and Computation, 2018, vol. 333, issue C, 490-505

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.

Keywords: Volterra integral equations; Renewal equations; Delay differential equations; Laguerre pseudospectral discretization; Physiologically structured population models; Finite dimensional state representation; Infinite delay (search for similar items in EconPapers)
Date: 2018
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:333:y:2018:i:c:p:490-505

DOI: 10.1016/j.amc.2018.03.104

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