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

Abstract  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.

• Content Type Journal Article
• DOI 10.1007/s00211-009-0281-z
• Authors
  
  
  • Wansheng Wang, Huazhong University of Science and Technology School of Mathematics and Statistics 430074 Wuhan China
  • Chengjian Zhang, Huazhong University of Science and Technology School of Mathematics and Statistics 430074 Wuhan China
  
  

• Journal Numerische Mathematik
• Online ISSN 0945-3245
• Print ISSN 0029-599X

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Original source : http://www.springerlink.com/content/d8455v183vm422...