期刊论文

Wang, Wansheng

英文

Applied Mathematics and Computation

0096-3003

2017

314

380-390

10.1016/j.amc.2017.07.013

This work was supported by the National Natural Science Foundation of China (grant no. 11371074) and the Natural Science Foundation of Hunan Province for Distinguished Young scholars, China (grant no. 13JJ1020), and the Research Foundation of Education Bureau of Hunan Province, China (grant no. 13A108).

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This paper is concerned with the stability of the one-leg methods for nonlinear Volterra functional differential equations (VFDEs). The contractivity and asymptotic stability properties are first analyzed for quasi-equivalent and A-stable one-leg methods by use of two lemmas proven in this paper. To extend the analysis to the case of strongly A-stable one-leg methods, Nevanlinna and Liniger's technique of introducing new norm is used to obtain the conditions for contractivity and asymptotic stability of these methods. As a consequence, it is shown that one-leg theta-methods (theta is an elemen...