High Order Contractive Runge-Kutta Methods for Volterra Functional Differential Equations

Authors:
Shoufu Li
Affiliations:
lisf@xtu.edu.cn
Venue:
SIAM Journal on Numerical Analysis
Year:
2010

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Abstract

A contractivity theory of Runge-Kutta methods for stiff nonlinear Volterra functional differential equations (VFDEs) is established, by means of which a family of high order contractive Runge-Kutta methods for VFDEs are identified. The application of the general theory for stiff nonlinear VFDEs to the special cases of stiff nonlinear delay differential equations and delay integro-differential equations is also presented.