The effect of quadrature on the dynamics of a discretized nonlinear integro-differential equation
type: Item
instance of: scholarly article
title: The effect of quadrature on the dynamics of a discretized nonlinear integro-differential equation
zbMATH Open document ID: 0946.65136
DOI: 10.1016/S0168-9274(99)00013-6
author: Mark A. Aves
author: Penny J. Davies
author: Desmond J. Higham
published in: Applied Numerical Mathematics
publication date: 2000-10-10T00:00:00Z
review text: The integro-differential equation of population dynamics \[ \phi'(t)=\phi(t)\left(1-\int_{-\infty}^tK(t-\tau)\phi(\tau)d\tau\right), \enskip t>0 \] with convolution kernel is studied. The Euler approximation implies a discrete model. The existence and stability of fixed and periodic points are investigated. The analysis of spurious periodic solutions and numerical results are given. In conclusion an adaptive algorithm based on local error control is developed.
reviewed by: Nikolai Pleshchinskii
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45J05
Mathematics Subject Classification ID: 45G05
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 1399546
zbMATH Keywords: integro-differential equation
zbMATH Keywords: population dynamics
zbMATH Keywords: convolution kernel
zbMATH Keywords: long-term dynamics
zbMATH Keywords: spurious solution
zbMATH Keywords: error control
zbMATH Keywords: Euler method
zbMATH Keywords: fixed point
zbMATH Keywords: stability
zbMATH Keywords: periodic points
zbMATH Keywords: periodic solutions
zbMATH Keywords: numerical results
zbMATH Keywords: adaptive algorithm
Wikidata QID: Q115339508
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1399546