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

作者：Li; Shoufu

来源：Frontiers of Mathematics in China, 2009, 4(1): 23-48.

DOI：10.1007/s11464-009-0003-y

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

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), delay-integrodifferential equations (DIDEs) and VFDEs of other type which appear in practice.

• 出版日期2009-3
• 单位湘潭大学