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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

On the correctness of partial differential operators and the von Neumann condition for stability of finite difference operators


Author: D. G. Aronson
Journal: Proc. Amer. Math. Soc. 14 (1963), 948-955
MSC: Primary 65.65
MathSciNet review: 0156484
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  • [1] D. G. Aronson, The stability of finite difference approximations to second order linear parabolic differential equations, Duke Math. J. 30 (1963), 117–127. MR 0145681 (26 #3210)
  • [2] D. G. Aronson, On the stability of certain finite difference approximations to parabolic systems of differential equations, Numer. Math. 5 (1963), 118-137; correction, ibid. 5 (1963), 290. MR 0156485 (27 #6408)
  • [3] I. M. Gel'fand and G. E. Šilov, Generalized functions, Part 3, Gosudarstv. Izdat. Fiz.-Mat. Lit., Moscow, 1958. (Russian)
  • [4] Fritz John, On integration of parabolic equations by difference methods. I. Linear and quasi-linear equations for the infinite interval, Comm. Pure Appl. Math. 5 (1952), 155–211. MR 0047885 (13,947b)
  • [5] Heinz-Otto Kreiss, Über die Approximative Lösung von linearen partiellen Differentialgleichungen mit Hilfe von Differenzengleichungen, Kungl. Tekn. Högsk. Handl. Stockholm 128 (1958), 1-19.
  • [6] Heniz-Otto Kreiss, Über die Lösung des Cauchyproblems für lineare partielle Differentialgleichungen mit Hilfe von Differenzengleichungen. I. Stabile Systeme von Differenzengleichungen, Acta Math. 101 (1959), 179–199 (German). MR 0130474 (24 #A335)
  • [7] Robert D. Richtmyer, Difference methods for initial-value problems, Interscience tracts in pure and applied mathematics. Iract 4, Interscience Publishers, Inc., New. York, 1957. MR 0093918 (20 #438)
  • [8] V. S. Rjabenki and A. F. Filippow, Über die Stabilität von Differenzengleichungen, Mathematik für Naturwissenschaft und Technik, Bd. 3. VEB Deutscher Verlag der Wissenschaften, Berlin, 1960 (German). MR 0123106 (23 #A437)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1963-0156484-7
PII: S 0002-9939(1963)0156484-7
Article copyright: © Copyright 1963 American Mathematical Society