Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-1963-0156484-7
MathSciNet review: 0156484
Full-text PDF Free Access

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [1] D. G. Aronson, The stability of finite difference approximations to second order linear parabolic differential equations, Duke Math. J. 30 (1963), 117-128. MR 0145681 (26:3210)
  • [2] -, On the stability of certain finite difference approximations to parabolic systems of differential equations, Numer. Math. 5 (1963), 118-137, 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, 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] -, Über die Lösung des Cauchyproblems für lineare partielle Differentialgleichungen mit Hilfe von Differenzengleichungen. 1, Acta Math. 101 (1959), 179-199. MR 0130474 (24:A335)
  • [7] R. D. Richtmyer, Difference methods for initial-value problems, Interscience Tracts in Pure and Applied Mathematics. Tract 4. Interscience, New York, 1957. MR 0093918 (20:438)
  • [8] V. S. Rjaben'kiĭ and A. F. Filippov, On stability of difference equations, GITTL, Moscow, 1956 (Russian); German transl., Über die Stabilität von Differenzengleichungen, Berlin, 1960. MR 0123106 (23:A437)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 65.65

Retrieve articles in all journals with MSC: 65.65


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1963-0156484-7
Article copyright: © Copyright 1963 American Mathematical Society

American Mathematical Society