Numerische Mathematik

, Volume 115, Issue 3, pp 451–474

Preserving stability implicit Euler method for nonlinear Volterra and neutral functional differential equations in Banach space


DOI: 10.1007/s00211-009-0281-z

Cite this article as:
Wang, W. & Zhang, C. Numer. Math. (2010) 115: 451. doi:10.1007/s00211-009-0281-z


This paper is concerned with the contractivity and asymptotic stability properties of the implicit Euler method (IEM) for nonlinear functional differential equations (FDEs). These properties are first analyzed for Volterra FDEs and then the analysis is extended to the case of neutral FDEs (NFDEs). Such an extension is particularly important since NFDEs are more general and have received little attention in the literature. The main result we establish is that the IEM with linear interpolation can completely preserve these stability properties of the analytical solution to such FDEs.

Mathematics Subject Classification (2000)

65L20 65L05 

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsHuazhong University of Science and TechnologyWuhanChina
  2. 2.School of Mathematics and Computational ScienceChangsha University of Science and TechnologyChangshaChina