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Stability analysis of Runge-Kutta methods for Volterra integral equations of the second kind. (English) Zbl 0686.65095
A general class of Runge-Kutta type methods for the numerical solution of second kind Volterra integral equations is considered. The authors present a stability analysis for the test equation $$y(t)=1+\int^{t}_{0}(\lambda +\sigma (t-s))y(s)ds$$ with either $$\sigma =0$$ and $$\lambda$$ complex, or $$\lambda$$ and $$\sigma$$ both real. As an application they construct families of $$V_ 0$$-stable methods of orders one and two $$(V_ 0$$-stability means that for $$\lambda <0$$ and $$\sigma <0$$ the numerical solution satisfies $$y_ n\to 0$$ for all step sizes $$h>0)$$.
Reviewer: E.Hairer

MSC:
 65R20 Numerical methods for integral equations 45D05 Volterra integral equations
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