First occurrence prime gaps

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

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

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
Volume52
Issue number185
DOIs
StatePublished - 1989

Fingerprint

Continuous Extension
Runge Kutta methods
Natural Extension
Runge-Kutta Methods
Piecewise Polynomials
Volterra Integral Equations
Approximation
Polynomial function
Integral equations
Tail
Polynomials
Numerical Solution
kernel
Grid
Interval
Evaluation
Class

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

Cite this

First occurrence prime gaps. / Bellen, A.; Jackiewicz, Zdzislaw; Vermiglio, R.; Zennaro, M.

In: Mathematics of Computation, Vol. 52, No. 185, 1989, p. 49-63.

Research output: Contribution to journalArticle

Bellen, A, Jackiewicz, Z, Vermiglio, R & Zennaro, M 1989, 'First occurrence prime gaps', Mathematics of Computation, vol. 52, no. 185, pp. 49-63. https://doi.org/10.1090/S0025-5718-1989-0971402-3
Bellen, A. ; Jackiewicz, Zdzislaw ; Vermiglio, R. ; Zennaro, M. / First occurrence prime gaps. In: Mathematics of Computation. 1989 ; Vol. 52, No. 185. pp. 49-63.
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