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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

An algorithm for the solution of certain differential-difference equations of advanced type


Author: G. Greaves
Journal: Math. Comp. 38 (1982), 237-247
MSC: Primary 65R20; Secondary 10H30
MathSciNet review: 637302
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Abstract | References | Similar Articles | Additional Information

Abstract: The differential-difference problem

$\displaystyle \frac{d}{{ds}}\;\{ {sJ(s)} \} + J(s + 1) = 0\;(\operatorname{Re} (s) > 0);\quad sJ(s) \to 1\;{\text{as}}\;s \to 0,$

which arises in the theory of numbers, is studied and an algorithm developed for the simultaneous numerical approximation of the derivatives $ {J^{(n)}}(s)$. An error bound is established for the process described and its numerical performance and stability are discussed.

References [Enhancements On Off] (What's this?)

  • [1] Richard Bellman and Kenneth L. Cooke, Differential-difference equations, Academic Press, New York-London, 1963. MR 0147745 (26 #5259)
  • [2] N. G. De Bruijn, On the number of uncancelled elements in the sieve of Eratosthenes, Nederl. Akad. Wetensch., Proc. 53 (1950), 803–812 = Indagationes Math. 12, 247–256 (1950). MR 0035785 (12,11d)
  • [3] N. G. de Bruijn, On the number of positive integers ≤𝑥 and free of prime factors >𝑦, Nederl. Acad. Wetensch. Proc. Ser. A. 54 (1951), 50–60. MR 0046375 (13,724e)
  • [4] K. Dickman, ``On the frequency of numbers containing prime factors of a certain relative magnitude,'' Ark. Mat., v. 22A, 1930, pp. 1-14.
  • [5] G. Greaves, A weighted sieve of Brun’s type, Acta Arith. 40 (1981/82), no. 3, 297–332. MR 664619 (83m:10082)
  • [6] Henryk Iwaniec, Rosser’s sieve, Acta Arith. 36 (1980), no. 2, 171–202. MR 581917 (81m:10086)
  • [7] H. Iwaniec, J. van der Lune & H. J. J. te Riele, ``The limits of Buchstab's iteration sieve,'' Nederl. Akad. Wetensch. Proc. Ser. A, v. 83, 1980, pp. 409-417.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1982-0637302-7
PII: S 0025-5718(1982)0637302-7
Article copyright: © Copyright 1982 American Mathematical Society