A review of theoretical and numerical analysis for nonlinear stiff Volterra functional differential equations |
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Authors: | Shoufu Li |
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Institution: | Department of Mathematics, Xiangtan University, Xiangtan 411105, China |
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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.
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Keywords: | Nonlinear stiff problem functional differential equation stability contractivity asymptotic stability Runge-Kutta method |
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