文章基本信息

标题：Dissipativity of the backward Euler method for nonlinear Volterra functional differential equations in Banach space
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作者：Siqing Gan
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2015
卷号：2015
期号：1
页码：128
DOI：10.1186/s13662-015-0469-8
语种：English
出版社：Hindawi Publishing Corporation
摘要：This paper concerns the dissipativity of nonlinear Volterra functional differential equations (VFDEs) in Banach space and their numerical discretization. We derive sufficient conditions for the dissipativity of nonlinear VFDEs. The general results provide a unified theoretical treatment for dissipativity analysis to ordinary differential equations (ODEs), delay differential equations (DDEs), integro-differential equations (IDEs) and VFDEs of other type appearing in practice. Then the dissipativity property of the backward Euler method for VFDEs is investigated. It is shown that the method can inherit the dissipativity of the underlying system. The close relationship between the absorbing set of the numerically discrete system generated by the backward Euler method and that of the underlying system is revealed.
关键词：dissipativity ; Volterra functional differential equation ; Banach space ; backward Euler method