First occurrence prime gaps

A. Bellen, Zdzislaw Jackiewicz, R. Vermiglio, M. Zennaro

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


We consider a very general class of Runge-Kutta methods for the numerical solution of Volterra integral equations of the second kind, which includes as special cases all the more important methods which have been considered in the literature. The main purpose of this paper is to define and prove the existence of the Natural Continuous Extensions (NCE’s) of Runge-Kutta methods, i.e., piecewise polynomial functions which extend the approximation at the grid points to the whole interval of integration. The particular properties required of the NCE’s allow us to construct the tail approximations, which are quite efficient in terms of kernel evaluations.

Original languageEnglish (US)
Pages (from-to)49-63
Number of pages15
JournalMathematics of Computation
Issue number185
StatePublished - 1989

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

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