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Mathematics of Computation

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Convergence rates of iterative treatments of partial differential equations

Author: Stanley P. Frankel
Journal: Math. Comp. 4 (1950), 65-75
MSC: Primary 65.0X
Corrigendum: Math. Comp. 5 (1951), 184.
MathSciNet review: 0046149
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References [Enhancements On Off] (What's this?)

  • [1] D. R. Hartree, ``The ENIAC an electronic computing machine,'' Nature, v. 158, 1946, p. 500-506. [MTAC, v. 2, p. 222] IBM Automatic Sequence Controlled Calculator, IBM Corporation, New York, 1945. Anon., ``The UNIVAC,'' Electronic Industries, v. 2, 1948, p. 9. H. H. Goldstine & J. von Neumann, Planning and Coding of Problems for an Electronic Instrument, Institute for Advanced Study, Princeton, 1947. [MTAC, v. 3, p. 54-56] MR 0018978 (8:355a)
  • [2] R. V. Southwell, Relaxation Methods in Engineering Science, Oxford, 1940.
  • [3] E. T. Whittaker & G. Robinson, The Calculus of Observations, London and Glasgow, 1932.
  • [4] G. Shortley, R. Weller, & B. Fried, ``Numerical solution of Laplace's and Poisson 's equations with applications to photoelasticity and torsion,'' Ohio State University, Studies, Engineering Series, Bull. no. 107, 1942.
  • [5] L. F. Richardson, ``The approximate arithmetical solution by finite differences of physical problems involving differential equations, with an application to the stresses in a masonry dam,'' R. Soc., London, Phil. Trans. s. A, v. 210, 1911, p. 307-357. ``How to solve differential equations approximately by arithmetic,'' Math. Gazette, v. 12, p. 415-421, 1925.
  • [6] R. Courant, ``Über partielle Differenzengleichungen,'' Congresso Internazionale dei Matematici, Atti, Bologna, v. 3, 1930, p. 83-89.
  • [7] This can be shown by the method used by H. Lewy in ``On the convergence of solutions of difference equations,'' Studies and Essays Presented to R. Courant on his 60th Birthday, New York, 1948, p. 211-214. MR 0022988 (9:288d)
  • [8] H. Liebmann, ``Die angenäherte Ermittelung harmonischer Funktionen und konformer Abbildungen,'' Bayer. Akad. Wiss., math.-phys. Klasse, Sitz., 1918, p. 385-416 Further references to the Liebmann method are cited in footnote 1 of Shortley, Weller & Fried. See also MTAC v. 3, p. 350, footnote 3.

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Article copyright: © Copyright 1950 American Mathematical Society

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