Abstract
In this paper, we investigate highly stable multistep Runge–Kutta methods for Volterra integral equations. First, the order conditions for order p and stage order $$q=p$$ are presented, and a convergence theorem is given. The numerical stability conditions for the basic and convolution test equations are derived. Then, the methods with one or two stages are studied in detail. Some A-stable and $$V_0$$ -stable m-stage methods with order $$p>m$$ are obtained. For one-stage methods, we also construct $$A_0$$ -stable and -stable methods of orders 3 and 4. Finally, numerical experiments are given to confirm the theoretical results.
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