SURVEY ARTICLE

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

  • Shoufu LI
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  • Department of Mathematics, Xiangtan University, Xiangtan 411105, China

Received date: 20 Jan 2008

Accepted date: 04 Sep 2008

Published date: 05 Mar 2009

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

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.

Cite this article

Shoufu LI . A review of theoretical and numerical analysis for nonlinear stiff Volterra functional differential equations[J]. Frontiers of Mathematics in China, 2009 , 4(1) : 23 -48 . DOI: 10.1007/s11464-009-0003-y

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