Applied Mathematics and Computation ( IF 4 ) Pub Date : 2021-10-09 , DOI: 10.1016/j.amc.2021.126686 Magdalena Nockowska-Rosiak 1 , Christian Pötzsche 2
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.
中文翻译:
Urysohn 积分算子的单调性和离散化
Banach 空间上的非线性算子保持有序关系的性质,是次齐次或有序凹的,而有序锥则具有深远的影响。在非线性分析中,它允许通过合适的不动点或单调迭代技术来求解相关方程。在动力系统中,关联积分微分方程可能的长期行为被极大地简化了。本文包含向量值 Urysohn 积分算子为单调、次齐次或凹的充分条件。它还提供了保证这些属性在特别是 Nyström 类型的空间离散化下保留的条件。这一事实对于数值方案收敛或模拟再现实际行为和渐近线至关重要。