Dissipativity of the backward Euler method for nonlinear Volterra functional differential equations in Banach space

Advances in Difference Equations

Siqing Gan¹ 

[1] School of Mathematics and Statistics, Central South University, Changsha, China

关键词: dissipativity;    Volterra functional differential equation;    Banach space;    backward Euler method;   

DOI  :  10.1186/s13662-015-0469-8

学科分类：数学（综合）

来源: SpringerOpen

【 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.

【 授权许可】

CC BY