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Mathematics of Computation

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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
DOI: https://doi.org/10.1090/S0025-5718-1982-0637302-7
MathSciNet review: 637302
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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.

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DOI: https://doi.org/10.1090/S0025-5718-1982-0637302-7
Article copyright: © Copyright 1982 American Mathematical Society

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