Numerical dynamics of integrodifference equations: Basics and discretization errors in a C0-setting

Christian Pötzsche

Applied Mathematics and Computation, 2019, vol. 354, issue C, 422-443

Abstract: Besides being interesting infinite-dimensional dynamical systems in discrete time, integrodifference equations successfully model growth and dispersal of populations with nonoverlapping generations, and are often illustrated by simulations. This paper points towards and initiates a mathematical foundation of such simulations using generic methods to numerically discretize (and solve) integral equations. We tackle basic properties of a flexible class of integrodifference equations, as well as of their collocation and degenerate kernel semi-discretizations on the state space of continuous functions over a compact domain. Moreover, various estimates for the global discretization error are provided. Numerical simulations illustrate and confirm our theoretical results.

Keywords: Integrodifference equation; Collocation method; Degenerate kernel method; Piecewise linear splines; Global discretization error (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:354:y:2019:i:c:p:422-443

DOI: 10.1016/j.amc.2019.02.033

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