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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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  • D. G. Aronson, The stability of finite difference approximations to second order linear parabolic differential equations, Duke Math. J. 30 (1963), 117–127. MR 145681
  • 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 156485, DOI
  • I. M. Gel’fand and G. E. Šilov, Generalized functions, Part 3, Gosudarstv. Izdat. Fiz.-Mat. Lit., Moscow, 1958. (Russian)
  • 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 47885, DOI
  • Heinz-Otto Kreiss, Über die Approximative Lösung von linearen partiellen Differentialgleichungen mit Hilfe von Differenzengleichungen, Kungl. Tekn. Högsk. Handl. Stockholm 128 (1958), 1-19.
  • 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 130474, DOI
  • Robert D. Richtmyer, Difference methods for initial-value problems, Interscience Tracts in Pure and Applied Mathematics, Tract 4, Interscience Publishers, Inc., New. York, 1957. MR 0093918
  • V. S. Rjabenki and A. F. Filippov, Über die Stabilität von Differenzengleichungen, Mathematik für Naturwissenschaft und Technik, Bd. 3. VEB Deutscher Verlag der Wissenschaften, Berlin, 1960 (German). MR 0123106

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Article copyright: © Copyright 1963 American Mathematical Society