Periodic solutions of non-linear discrete Volterra equations with finite memory

C. T H Baker, Yihong Song

    Research output: Contribution to journalArticlepeer-review


    In this paper we discuss the existence of periodic solutions of discrete (and discretized) non-linear Volterra equations with finite memory. The literature contains a number of results on periodic solutions of non-linear Volterra integral equations with finite memory, of a type that arises in biomathematics. The "summation" equations studied here can arise as discrete models in their own right but are (as we demonstrate) of a type that arise from the discretization of such integral equations. Our main results are in two parts: (i) results for discrete equations and (ii) consequences for quadrature methods applied to integral equations. The first set of results are obtained using a variety of fixed-point theorems. The second set of results address the preservation of properties of integral equations on discretizing them. The effect of weak singularities is addressed in a final section. The detail that is presented, which is supplemented using appendices, reflects the differing prerequisites of functional analysis and numerical analysis that contribute to the outcomes. © 2010 Elsevier B.V. All rights reserved.
    Original languageEnglish
    Pages (from-to)2683-2698
    Number of pages15
    JournalJournal of Computational and Applied Mathematics
    Issue number9
    Publication statusPublished - 1 Sept 2010


    • Discrete equations
    • Finite memory
    • Fixed-point theorems
    • Periodic solutions
    • Quadrature
    • Simulation
    • Weak singularities


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