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

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:234

Article

Baker, Christopher T. H.^2,3  Song, Yihong¹ 

[1] Suzhou Univ, Dept Math, Suzhou 215006, Jiangsu, Peoples R China

[2] Univ Chester, Dept Math, Chester CH1 4BJ, Cheshire, England

[3] Univ Manchester, Sch Math, Manchester M13 9PL, Lancs, England

关键词: Periodic solutions;    Discrete equations;    Finite memory;    Fixed-point theorems;    Quadrature;    Weak singularities;    Simulation;   

DOI  :  10.1016/j.cam.2010.01.019

来源: Elsevier

【 摘 要 】

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. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

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