Izzo, G.; Russo, E.; Chiapparelli, C. Highly stable Runge-Kutta methods for Volterra integral equations. (English) Zbl 1243.65157 Appl. Numer. Math. 62, No. 8, 1002-1013 (2012). Summary: We investigate the numerical stability of the class of Runge-Kutta methods for the solution of Volterra integral equations of the second kind. To this aim we introduce the definition of \(V_{0}(\alpha )\)-stability and a new technique to construct highly stable methods. \(V_{0}\)-stable methods of order three and four are provided. Cited in 9 Documents MSC: 65R20 Numerical methods for integral equations 45D05 Volterra integral equations 45G10 Other nonlinear integral equations Keywords:Runge-Kutta methods; nonlinear Volterra integral equations; linear stability analysis; convolution test equation; \(V_{0}\)-stability; \(V_{0}(\alpha )\)-stability; numerical examples Software:fminsearch × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Alexander, R., Diagonally implicit Runge-Kutta methods for stiff O.D.E.ʼs, SIAM J. Numer. Anal., 14, 6, 1006-1021 (1977) · Zbl 0374.65038 [2] Amini, S., Stability analysis of methods employing reducible rules for Volterra integral equations, BIT, 23, 322-328 (1983) · Zbl 0513.65084 [3] Baker, C. T.H.; Keech, M. S., Stability regions in the numerical treatment of Volterra integral equations, SIAM J. Numer. 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