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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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