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Stability of continuous Runge-Kutta-type methods for nonlinear neutral delay-differential equations. (English) Zbl 1205.65214
Summary: This paper provides results on the correct simulation, when using continuous Runge-Kutta methods, of certain stability properties of nonlinear neutral delay-differential equations (NDDEs) y ' (t)=f(t,y(t),y(t-τ(t)), y ' (t-τ(t))) tt 0 ). In particular, it is shown that certain continuous Runge-Kutta methods based upon the backward Euler method or the 2-stage Lobatto IIIC method, combined with linear interpolation, are GRN-stable and asymptotically stable for NDDEs.
65L06Multistep, Runge-Kutta, and extrapolation methods
34K25Asymptotic theory of functional-differential equations
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