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Frontiers of Mathematics in China

, Volume 4, Issue 1, pp 23–48 | Cite as

A review of theoretical and numerical analysis for nonlinear stiff Volterra functional differential equations

  • Shoufu LiEmail author
Survey Article

Abstract

In this review, we present the recent work of the author in comparison with various related results obtained by other authors in literature. We first recall the stability, contractivity and asymptotic stability results of the true solution to nonlinear stiff Volterra functional differential equations (VFDEs), then a series of stability, contractivity, asymptotic stability and B-convergence results of Runge-Kutta methods for VFDEs is presented in detail. This work provides a unified theoretical foundation for the theoretical and numerical analysis of nonlinear stiff problems in delay differential equations (DDEs), integro-differential equations (IDEs), delayintegro-differential equations (DIDEs) and VFDEs of other type which appear in practice.

Keywords

Nonlinear stiff problem functional differential equation stability contractivity asymptotic stability Runge-Kutta method 

MSC

65Q05 65R20 65L05 65L20 

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Copyright information

© Higher Education Press and Springer-Verlag GmbH 2009

Authors and Affiliations

  1. 1.Department of MathematicsXiangtan UniversityXiangtanChina

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