Skip to main content
Log in

The Galerkin method for singularly perturbed boundary value problems on adaptive grids

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Literature Cited

  1. A. B. Vasil'eva and V. F. Butuzov, Asymptotic Expansions of the Solutions of Singularly Perturbed Equations [in Russian], Nauka, Moscow (1973).

    Google Scholar 

  2. G. I. Marchuk and V. I. Agoshkov, Introduction to Projection-Grid Methods [in Russian], Nauka, Moscow (1981).

    Google Scholar 

  3. L. A. Oganesyan and L. A. Rukhovets, Variation-Difference Methods for Solving Elliptic Equations, Akad. Nauk ArmSSR, Erevan (1979).

    Google Scholar 

  4. S. G. Mikhlin, Variational Methods in Mathematical Physics [in Russian], Nauka, Moscow (1970).

    Google Scholar 

  5. U. Ascher and R. Weiss, “Collocation for singular perturbation problems. I. First order systems with constant coefficients,” SIAM J. Numer. Anal.,20, No. 3, 537–557 (1983).

    Google Scholar 

  6. C. Ringhofer, “On collocation schemes for quasilinear singularly perturbed boundary value problems,” SIAM J. Numer. Anal.,21, No. 5, 864–882 (1984).

    Google Scholar 

  7. I. A. Blatov and V. V. Strygin, Convergence of the collocation method for singularly perturbed boundary value problems. Manuscript deposited at VINITI, June 26, 1987, No. 4710-B87.

  8. I. A. Blatov and V. V. Strygin, “Convergence of the spline collocation method on optimal grids for singularly perturbed boundary value problems,” Differents. Uravn.,24, No. 11, 1977–1987 (1988).

    Google Scholar 

  9. N. S. Bakhvalov, “On the optimization of the methods for solving boundary value problems in the presence of a boundary layer,” Zh. Vychisl. Mat. i Mat. Fiz.,9, No. 4, 841–859 (1969).

    Google Scholar 

  10. Yu. S. Zav'yalov, B. I. Kvasov, and V. L. Miroshnichenko, Methods of Spline-Functions [in Russian], Nauka, Moscow (1980).

    Google Scholar 

  11. A. G. Baskakov, “On Banach algebras with nontrivial center,” in: Twelfth School on the Theory of Operators in Functional Spaces. Abstracts of Reports [in Russian], Tambov. Ped. Inst., Tambov (1987), p. 17.

    Google Scholar 

Download references

Authors

Additional information

Voronezh. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 31, No. 5, pp. 138–148, September–October, 1990.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Strygin, V.V., Sirunyan, V.V. The Galerkin method for singularly perturbed boundary value problems on adaptive grids. Sib Math J 31, 817–826 (1990). https://doi.org/10.1007/BF00974496

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00974496

Keywords

Navigation