Summary
Recently the author defined the class of natural Runge-Kutta methods and observed that it includes all the collocation methods. The present paper is devoted to a complete characterization of this class and it is shown that it coincides with the class of the projection methods in some polynomial spaces.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bellen, A., Jackiewicz, Z., Zennaro, M.: Stability analysis of one-step methods for neutral delay differential equations. Numer. Math.52, 605–619
Dekker, K., Verwer, J.G.: Stability of Runge-Kutta methods for stiff nonlinear differential equations. Amsterdam: North-Holland 1984
Jackiewicz, Z.: One-step methods of any order for neutral functional differential equations. SIAM J. Numer. Anal.21, 486–511 (1984)
Norsett, S.P., Wanner, G.: The real-pole sandwich for rational approximations and oscillation equations. Bl T19, 79–94 (1979)
Norsett, S.P., Wanner, G.: Perturbed collocation and Runge-Kutta methods. Numer. Math.38, 193–208 (1981)
Vermiglio, R.: A one-step subregion method for delay differential equations. Calcolo22, 429–455 (1985)
Zennaro, M.: Natural continuous extensions of Runge-Kutta methods. Math. Comput.46, 119–133 (1986)
Zennaro, M.:P-stability properties of Runge-Kutta methods for delay differential equations. Numer. Math.49, 305–318 (1986)
Author information
Authors and Affiliations
Additional information
This work was supported by the Italian Ministero della Pubblica Istruzione, funds 40%
Rights and permissions
About this article
Cite this article
Zennaro, M. Natural Runge-Kutta and projection methods. Numer. Math. 53, 423–438 (1988). https://doi.org/10.1007/BF01396327
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01396327