Nyström discretization of integrodifference equations: numerical continuation of periodic solutions and Floquet multipliers

Abstract

Integrodifference equations are discrete-time counterparts to reaction-diffusion equations and have various applications in, e.g., theoretical ecology. Their behavior is often illustrated using numerical simulations, which require a spatial discretization. In this paper, we establish that periodic solutions to time-periodic integrodifference equations, their stability and their Floquet spectrum persist under discretization of Nyström-type, which replaces integrals by quadrature or cubature rules. Moreover, it is shown that the convergence rates of the particular integration rules are preserved. By means of a typical model from theoretical ecology, these results are demonstrated in terms of a numerical continuation for periodic solutions and their Floquet multipliers.