 On A-stable one-leg methods for solving nonlinear Volterra functional differential equationsWansheng Wang Applied Mathematics and Computation, 2017, vol. 314, issue C, 380-390 Abstract: 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 θ-methods (θ ∈ (1/2, 1]) with linear interpolation are unconditionally contractive and asymptotically stable, and 2-step Adams type method and 2-step BDF method are conditionally contractive and asymptotically stable. The bounded stability of the midpoint rule is also proved with the help of the concept of semi-equivalent one-leg methods. Keywords: Nonlinear Volterra functional differential equations; Contractivity; Asymptotic stability; Bounded stability; One-leg methods; A-stability (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:314:y:2017:i:c:p:380-390 DOI: 10.1016/j.amc.2017.07.013 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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