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Monotonicity and discretization of Urysohn integral operators

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  • Nockowska-Rosiak, Magdalena
  • Pötzsche, Christian

Abstract

The property that a nonlinear operator on a Banach space preserves an order relation, is subhomogeneous or order concave w.r.t. an order cone has profound consequences. In Nonlinear Analysis it allows to solve related equations by means of suitable fixed point or monotone iteration techniques. In Dynamical Systems the possible long term behavior of associate integrodifference equations is drastically simplified. This paper contains sufficient conditions for vector-valued Urysohn integral operators to be monotone, subhomogeneous or concave. It also provides conditions guaranteeing that these properties are preserved under spatial discretization of particularly Nyström type. This fact is crucial for numerical schemes to converge, or for simulations to reproduce the actual behavior and asymptotics.

Suggested Citation

  • Nockowska-Rosiak, Magdalena & Pötzsche, Christian, 2022. "Monotonicity and discretization of Urysohn integral operators," Applied Mathematics and Computation, Elsevier, vol. 414(C).
    • Handle: RePEc:eee:apmaco:v:414:y:2022:i:c:s0096300321007700
    DOI: 10.1016/j.amc.2021.126686
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