Positivity and discretization of Fredholm integral operators

We provide sufficient conditions for vector-valued Fredholm integral operators and their commonly used spatial discretizations to be positive in terms of an order relation induced by a corresponding cone. It turns out that reasonable Nyström methods preserve positivity. Among the projection methods, persistence is obtained simplest ones based on polynomial, piecewise linear or specific cubic interpolation (collocation), as well constant basis functions Bubnov-Galerkin approach. However, semi-discretizations using quadratic splines sinc-collocation we demonstrate positivity violated. Our results are illustrated eigenpairs Krein-Rutman form investigations nonlinear operators.