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On the stability of the Ritz-Galerkin method for Hammerstein equations


Authors: Jörg Hertling and Alexandru I. Şchiop
Journal: Math. Comp. 29 (1975), 484-488
MSC: Primary 65R05
DOI: https://doi.org/10.1090/S0025-5718-1975-0383797-2
MathSciNet review: 0383797
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Abstract: For the numerical treatment of Hammerstein equations by variational methods which has been considered by Hertling, we establish the stability in the sense of Mikhlin, Stetter and Tucker.


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

  • [1] J. HERTLING, Numerical Treatment of Hammerstein-Equations by Variational Methods, R. Ansorge & W. Törnig (Eds.), Numerische Lösung nichtlinearer partieller Differential- und Integro-differentialgleichungen, Lecture Notes in Math., no. 267, Springer-Verlag, Berlin, 1972, pp. 267-288. MR 0351133 (50:3622)
  • [2] R. H. KASRIEL & M. Z. NASHED, "Stability of solutions of some classes of nonlinear operator equations," Proc. Amer. Math. Soc., v. 17, 1966, pp. 1036-1042. MR 33 #7896. MR 0199753 (33:7896)
  • [3] S. G. MIKHLIN, "On the stability of certain computational processes," Dokl. Akad. Nauk SSSR, v. 157, 1964, pp. 271-273 = Soviet Math. Dokl., v. 5, 1964, pp. 931-933. MR 31 #6361. MR 0182138 (31:6361)
  • [4] S. G. MIKHLIN, The Numerical Performance of Variational Methods, Wolters-Noordhoff, Groningen, 1971. MR 43 #4236. MR 0278506 (43:4236)
  • [5] A. I. ŞCHIOP, "Stability of Ritz procedure for nonlinear two-point boundary value problem," Numer. Math., v. 20, 1973, pp. 208-212. MR 0317552 (47:6099)
  • [6] H. J. STETTER, Analysis of Discretization Methods for Ordinary Differential Equations, Springer-Verlag, Berlin, 1973. MR 0426438 (54:14381)
  • [7] T. S. TUCKER, "Stability of nonlinear computing schemes," SIAM J. Numer. Anal., v. 6, 1969, pp. 72-81. MR 40 #3743. MR 0250509 (40:3743)
  • [8] M. M. VAINBERG, Variational Methods for the Study of Nonlinear Operators, Holden-Day, San Francisco, Calif., 1964. MR 31 #638. MR 0176364 (31:638)
  • [9] R. S. VARGA, Functional Analysis and Approximation Theory in Numerical Analysis, Regional Conference Series in Applied Mathematics, vol. 3, Soc. Indust. Appl. Math., Philadelphia, Pa., 1971. MR 0310504 (46:9602)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1975-0383797-2
Keywords: Hammerstein equation, Ritz-Galerkin method, stability of the numerical computation, finite element method
Article copyright: © Copyright 1975 American Mathematical Society

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