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Concerning periodic solutions to non-linear discrete Volterra equations with finite memory
Baker, Christopher T. H. Song, Yihong
Baker, Christopher T. H.
Song, Yihong
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2007
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Abstract
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. An expository style is adopted and examples are given to illustrate the discussion.
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Chester : University of Chester, 2007
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University of Chester
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en
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Applied Mathematics Group Research Report
2007 : 1
2007 : 1