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Compatible rate-of-convergence bounds for the grid method in the eigenvalue problem for the Helmholtz equation in a right triangle

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Abstract

An O(h) accurate difference scheme is constructed for the eigenvalue problem for the Helmholtz operator in a right triangle. The convergence of the difference scheme is analyzed under conditions ensuring that the eigenfunctions of the differential problem are in the space W 12 (Ω).

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References

  1. S. A. Voitsekhovskii, V. L. Makarov, and T. G. Shablii, “On convergence of difference solutions to generalized solutions of the Dirichlet problem for the Helmholtz equation in a convex polygon,” Zh. Vychisl. Matem. Mat. Fiz.,25, No. 9, 1336–1345 (1985).

    Google Scholar 

  2. O. A. Ladyzhenskaya and N. N. Ural'tseva, Linear and Quasilinear Elliptic Equations [in Russian], Nauka, Moscow (1973).

    Google Scholar 

  3. V. L. Makarov and V. G. Prikazchikov, “On the accuracy of the grid method in eigenvalue problems,” Differ. Uravn., No. 7, 1240–1244 (1982).

    Google Scholar 

  4. V. L. Makarov and A. A. Samarskii, “Application of exact difference schemes to estimate the rate of convergence of the method of lines,” Zh. Vychisl. Matem. Mat. Fiz.,20, No. 2, 371–387 (1980).

    Google Scholar 

  5. S. G. Mikhlin, Linear Partial Differential Equations [in Russian], Vysshaya Shkola, Moscow (1977).

    Google Scholar 

  6. V. G. Prikazchikov, “Difference eigenvalue problem for elliptic operator,” Zh. Vychisl. Matem. Mat. Fiz.,5, No. 4, 648–657 (1965).

    Google Scholar 

  7. A. A. Samarskii, “Accuracy of difference schemes for problems with generalized solutions,” in: Topical Problems of Mathematical Physics and Computational Mathematics [in Russian], Nauka, Moscow (1984), pp. 174–183.

    Google Scholar 

  8. V. I. Smirnov, A Course in Higher Mathematics [in Russian], Vol. 5, Fizmatgiz, Moscow (1959).

    Google Scholar 

  9. T. H. Bramble and S. R. Hulbert, “Bounds for a class of linear functionals with applications to Hermite polynomials,” Numer. Math.,16, No. 4, 362–365 (1971).

    Google Scholar 

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Authors and Affiliations

  1. Kiev University, USSR

    Yu. I. Rybak

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  1. Yu. I. Rybak
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Translated from Vychislitel'naya i Prikladnaya Matematika, No. 63, pp. 50–57, 1987.

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Rybak, Y.I. Compatible rate-of-convergence bounds for the grid method in the eigenvalue problem for the Helmholtz equation in a right triangle. J Math Sci 66, 2165–2171 (1993). https://doi.org/10.1007/BF01098601

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  • DOI: https://doi.org/10.1007/BF01098601

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