Convergence rates of iterative treatments of partial differential equations

Author:
Stanley P. Frankel

Journal:
Math. Comp. **4** (1950), 65-75

MSC:
Primary 65.0X

DOI:
https://doi.org/10.1090/S0025-5718-1950-0046149-3

Corrigendum:
Math. Comp. **5** (1951), 184.

MathSciNet review:
0046149

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References | Similar Articles | Additional Information

**[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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DOI:
https://doi.org/10.1090/S0025-5718-1950-0046149-3

Article copyright:
© Copyright 1950
American Mathematical Society