An algorithm for the solution of certain differentialdifference equations of advanced type
Author:
G. Greaves
Journal:
Math. Comp. 38 (1982), 237247
MSC:
Primary 65R20; Secondary 10H30
MathSciNet review:
637302
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Abstract 
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Abstract: The differentialdifference problem which arises in the theory of numbers, is studied and an algorithm developed for the simultaneous numerical approximation of the derivatives . An error bound is established for the process described and its numerical performance and stability are discussed.
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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. 409417.
 [1]
 R. Bellman & K. L. Cooke, DifferentialDifference Equations, Academic Press, 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., v. 53, 1950, pp. 803812 = Indag. Math., v. 12, 1950, pp. 247256. MR 0035785 (12:11d)
 [3]
 N. G. de Bruijn, ``On the number of positive integers and free of prime factors ,'' Nederl. Akad. Wetensch. Proc. Ser. A, v. 54, 1951, pp. 5060. 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. 114.
 [5]
 G. Greaves, ``A weighted sieve of Brun's type,'' Acta Arith., v. 40, 1981, pp. 301335. MR 664619 (83m:10082)
 [6]
 H. Iwaniec, ``Rosser's Sieve,'' Acta Arith., v. 36, 1980, pp. 171202. 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. 409417.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198206373027
PII:
S 00255718(1982)06373027
Article copyright:
© Copyright 1982
American Mathematical Society
