Convergence rates of iterative treatments of partial differential equations
Author:
Stanley P. Frankel
Journal:
Math. Comp. 4 (1950), 6575
MSC:
Primary 65.0X
Corrigendum:
Math. Comp. 5 (1951), 184.
MathSciNet review:
0046149
Fulltext PDF Free Access
References 
Similar Articles 
Additional Information
 [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. 307357. ``How to solve differential equations approximately by arithmetic,'' Math. Gazette, v. 12, p. 415421, 1925.
 [6]
R. Courant, ``Über partielle Differenzengleichungen,'' Congresso Internazionale dei Matematici, Atti, Bologna, v. 3, 1930, p. 8389.
 [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. 385416 Further references to the Liebmann method are cited in footnote 1 of Shortley, Weller & Fried. See also MTAC v. 3, p. 350, footnote 3.
 [1]
 D. R. Hartree, ``The ENIAC an electronic computing machine,'' Nature, v. 158, 1946, p. 500506. [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. 5456] 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. 307357. ``How to solve differential equations approximately by arithmetic,'' Math. Gazette, v. 12, p. 415421, 1925.
 [6]
 R. Courant, ``Über partielle Differenzengleichungen,'' Congresso Internazionale dei Matematici, Atti, Bologna, v. 3, 1930, p. 8389.
 [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. 211214. MR 0022988 (9:288d)
 [8]
 H. Liebmann, ``Die angenäherte Ermittelung harmonischer Funktionen und konformer Abbildungen,'' Bayer. Akad. Wiss., math.phys. Klasse, Sitz., 1918, p. 385416 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/S00255718195000461493
PII:
S 00255718(1950)00461493
Article copyright:
© Copyright 1950
American Mathematical Society
