Asymptotic periodicity of nonlinear discrete Volterra equations and applications

Abstract

Sufficient conditions for the asymptotic periodicity of solutions of nonlinear discrete Volterra equations of Hammerstein type are obtained. Such results are applied to analyze the property of a class of numerical methods to preserve the asymptotic periodicity of the analytical solution of Volterra integral equations

Exponential fitting quadrature rule for functional equations

“…These integrals arise, for example, in the numerical solution of Volterra integral equations (VIEs) with periodic solution, which model a considerable variety of periodic phenomena, as for example the spread of epidemics [1][2][3][4], hereditary response in continuum physics for a material with large memory [5], feedback systems with periodic input [6]. A successful strategy in the numerical treatment of oscillatory functions has been furnished by the theory of exponential fitting, introduced in [7] (see also the monograph [8]).…”