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

 

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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  • [1] D. R. Hartree, The ENIAC, an electronic computing machine, Nature 158 (1946), 500–506. 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] Hans Lewy, On the convergence of solutions of difference equations, Studies and Essays Presented to R. Courant on his 60th Birthday, January 8, 1948, Interscience Publishers, Inc., New York, 1948, pp. 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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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1950-0046149-3
PII: S 0025-5718(1950)0046149-3
Article copyright: © Copyright 1950 American Mathematical Society