Abstract
Two families of implicit Runge-Kutta methods with higher derivatives are (re-)considered generalizing classical Runge-Kutta methods of Butcher type and f Ehle type. For generalized Butcher methods the characteristic functionG(η) is represented by means of the node polynomial directly, thereby showing that in methods of maximum order,G(η) is connected withs-orthogonal polynomials in exactly the same way as Padé approximations in the classical case.
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Gekeler, E.W. On implicit Runge-Kutta methods with higher derivatives. BIT 28, 809–816 (1988). https://doi.org/10.1007/BF01954901
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DOI: https://doi.org/10.1007/BF01954901