Equations with infinite delay: Numerical bifurcation analysis via pseudospectral discretization

Autor: Mats Gyllenberg, Francesca Scarabel, Rossana Vermiglio
Přispěvatelé: Department of Mathematics and Statistics
Rok vydání: 2018
Předmět:
Delay differential equations
Physiologically structured population models
Discretization
Volterra integral equations
MODELS
MathematicsofComputing_NUMERICALANALYSIS
010103 numerical & computational mathematics
Laguerre pseudospectral discretization
01 natural sciences
Volterra integral equation
Volterra integral equations Renewal equations Delay differential equations Laguerre pseudospectral discretization Physiologically structured population models Finite dimensional state representation Infinite delay
010305 fluids & plasmas
symbols.namesake
Software
DUAL SEMIGROUPS
ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION
0103 physical sciences
Convergence (routing)
111 Mathematics
Applied mathematics
0101 mathematics
Perturbation theory
Mathematics
business.industry
Applied Mathematics
Delay differential equation
Renewal equations
Computational Mathematics
Nonlinear system
infinite delay
Ordinary differential equation
symbols
PERTURBATION-THEORY
Finite dimensional state representation
business
GENERATION
Zdroj: Applied Mathematics and Computation. 333:490-505
ISSN: 0096-3003
DOI: 10.1016/j.amc.2018.03.104
Popis: 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.
Databáze: OpenAIRE
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