Iterative methods for solving partial difference equations of elliptic type
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- by David Young
- Trans. Amer. Math. Soc. 76 (1954), 92-111
- DOI: https://doi.org/10.1090/S0002-9947-1954-0059635-7
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References
- L. Collatz, Bemerkungen zur Fehlerabschätzung für das Differenzenverfahren bei partiellen Differentialgleichungen, Zeitschrift für Angewandte Mathematik und Mechanik vol. 13 (1933) pp. 56-57.
- Arnold Dresden, On the iteration of linear homogeneous transformations, Bull. Amer. Math. Soc. 48 (1942), 577–579. MR 6984, DOI 10.1090/S0002-9904-1942-07736-6
- Stanley P. Frankel, Convergence rates of iterative treatments of partial differential equations, Math. Tables Aids Comput. 4 (1950), 65–75. MR 46149, DOI 10.1090/S0025-5718-1950-0046149-3
- Hilda Geiringer, On the solution of systems of linear equations by certain iteration methods, J. W. Edwards, Ann Arbor, Michigan, 1948. MR 0029272 S. Gerschgorin, Fehlerabschätzung für das Differenzenverfahren zur Lösung partieller Differentialgleichungen, Zeitschrift für Angewandte Mathematik und Mechanik vol. 10 (1930) pp. 373-382. H. Liebmann, Die angenährte Ermittelung harmonischer Functionen und konformer Abbildungen, Sitzungsberichte der Mathematisch-Naturwissenschaftlichen Klasse der Bayerischen Akademie der Wissenschaften zu München (1918) pp. 385-416.
- L. M. Milne-Thomson, The Calculus of Finite Differences, Macmillan & Co., Ltd., London, 1951. MR 0043339
- Rufus Oldenburger, Infinite powers of matrices and characteristic roots, Duke Math. J. 6 (1940), 357–361. MR 1949 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, Philos. Trans. Roy. Soc. London vol. 210A (1910) pp. 307-357. L. Seidel, Über ein Verfahren die Gleichungen, auf welche die Methode der kleinsten Quadrate führt, sowie lineäre Gleichungen überhaupt durch successive Annäherung aufzulösen, Abhandlungen der Bayerischen Akademie vol. 11, Dritte Abteilung (1873) pp. 81-108. G. Shortley and R. Weller, The numerical solution of Laplace’s equation, Journal of Applied Physics vol. 9 (1938) pp. 334-344.
- Frances E. Snyder and Hubert M. Livingston, Coding of a Laplace boundary value problem for the UNIVAC, Math. Tables Aids Comput. 3 (1949), 341–350. MR 28691, DOI 10.1090/S0025-5718-1949-0028691-6
- R. V. Southwell, Relaxation Methods in Theoretical Physics, Oxford, at the Clarendon Press, 1946. MR 0018983 —, Relaxation methods as ancillary techniques, Proceedings of a Symposium on the Construction and Application of Conformal Maps, National Bureau of Standards, Applied Mathematics Series vol. 18 (1949) pp. 239-241.
- P. Stein and R. L. Rosenberg, On the solution of linear simultaneous equations by iteration, J. London Math. Soc. 23 (1948), 111–118. MR 28682, DOI 10.1112/jlms/s1-23.2.111 E. Titchmarsh, The theory of functions, Oxford University Press, 2d ed., 1939. R. von Mises and H. Geiringer, Praktische Verfahren der Gleichungsauflösung, Zusammenfassender Bericht. Zeitschrift für Angewandte Mathematik und Mechanik vol. 9 (1929) pp. 58-77 and pp. 152-164. J. Wedderburn, Lectures on matrices, Amer. Math. Soc. Colloquium Publications, vol. 17, New York, 1934. D. Young, The rate of convergence of an improved iterative method for solving the finite difference analogue of the Dirichlet problem, Bull. Amer. Math. Soc. Abstract 56-4-322. —, Iterative methods for solving partial difference equations of elliptic type, Doctoral Thesis, Harvard University, 1950. —, On Richardson’s method for solving linear systems with positive definite matrices, to appear in the Journal of Mathematics and Physics.
Bibliographic Information
- © Copyright 1954 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 76 (1954), 92-111
- MSC: Primary 65.0X
- DOI: https://doi.org/10.1090/S0002-9947-1954-0059635-7
- MathSciNet review: 0059635