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

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  • Pötzsche, Christian

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.

Suggested Citation

  • Pötzsche, Christian, 2019. "Numerical dynamics of integrodifference equations: Basics and discretization errors in a C0-setting," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 422-443.
    • Handle: RePEc:eee:apmaco:v:354:y:2019:i:c:p:422-443
    DOI: 10.1016/j.amc.2019.02.033
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