Abstract
AbstractIntegrodifference equations are versatile models in theoretical ecology for the spatial dispersal of species evolving in non-overlapping generations. The dynamics of these infinite-dimensional discrete dynamical systems is often illustrated using computational simulations. This paper studies the effect of Nyström discretization to the local dynamics of periodic integrodifference equations having Hölder continuous functions over a compact domain as state space. We prove persistence and convergence for hyperbolic periodic solutions and their associated stable and unstable manifolds respecting the convergence order of the quadrature/cubature method.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics
Reference33 articles.
1. Alouges, F., Debussche, A.: On the qualitative behavior of the orbits of a parabolic partial differential equation and its discretization in the neighborhood of a hyperbolic fixed point. Numer. Funct. Anal. Optim. 12(3–4), 253–269 (1991)
2. Series in Automatic Computation;PM Anselone,1971
3. Atkinson, K.E.: The numerical evaluation of fixed points for completely continuous operators. SIAM J. Numer. Anal. 10(5), 799–807 (1973)
4. Atkinson, K.E.: A survey of numerical methods for solving nonlinear integral equations. J. Integr. Equ. Appl. 4(1), 15–46 (1992)
5. Baumgärtel, H.: Analytic Perturbation Theory for Matrices and Operators, Operator Theory: Advances and Applications, vol. 15. Birkhäuser, Basel (1985)