Frontiers of Mathematics in China >
A review of theoretical and numerical analysis for nonlinear stiff Volterra functional differential equations
Received date: 20 Jan 2008
Accepted date: 04 Sep 2008
Published date: 05 Mar 2009
Copyright
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.
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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