Advertisement

Siberian Mathematical Journal

, Volume 34, Issue 1, pp 10–24 | Cite as

Fourth order accuracy collocation method for singularly perturbed boundary value problems

  • I. A. Blatov
  • V. V. Strygin
Article

Keywords

Fourth Order Collocation Method Order Accuracy Fourth Order Accuracy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Yu. S. Zav'yalov, B. I. Kvasov, and V. L. Miroshnichenko, Methods of Spline Functions [in Russian], Nauka, Moscow (1980).Google Scholar
  2. 2.
    I. A. Blatov and V. V. Strygin, “Convergence of the spline collocation method on optimal meshes for singularly perturbed boundary value problems,” Differentsial'nye Uravneniya,24 No. 11, 1977–1987 (1988).Google Scholar
  3. 3.
    I. A. Blatov and V. V. Strygin “Convergence of collocation method for singularly perturbed boundary value problems on locally uniform N. S. Bakhvalov's meshes,” submitted to VINITI on July 11, 1989, No. 4996-B89.Google Scholar
  4. 4.
    K. Surla and D. Herceg, “Exponential spline difference scheme for singular perturbation problem,” in: Splines Numer. Anal. Conf. Int. Sem. ISAM-89, Weisig, April 24–28, 1989, Berlin, 1989, pp. 171–180.Google Scholar
  5. 5.
    M. Stojanovic and M. Kulpinski, “A quadratic spline collocation method for singular two-point boundary value problems,” Zb. Rad.,3, 43–49 (1989).Google Scholar
  6. 6.
    J. W. Daniel and B. K. Swartz, “Extrapolated collocation for two-point boundary value problems using cubic splines,” J. Inst. Math. Appl.,16, 161–174 (1975).Google Scholar
  7. 7.
    N. S. Bakhvalov, “On optimization of methods of 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
  8. 8.
    G. M. Vaînikko, Compact Approximation and Approximate Solution to Operator Equations [in Russian], Tartu University, Tartu (1970).Google Scholar
  9. 9.
    I. A. Blatov and V. V. Strygin, “The convergence of the Galërkin method for nonlinear two-point singularly perturbed boundary value problem in the spaceC[a,b],” Zh. Vychisl. Mat. i Mat. Fiz.,25, No. 7, 1001–1009 (1985).Google Scholar
  10. 10.
    I. A. Blatov, “On the projection method for singularly perturbed boundary value problems,” zh. Vychisl. Mat. i Mat. Fiz.,30, No. 7, 1131–1144 (1990).Google Scholar
  11. 11.
    M. I. Vishik and L. A. Lyusternik, “Regular generation and a boundary layer for nonlinear differential equations with a small parameter,” Uspekhi Mat. Nauk,12, No. 5, 3–122 (1957).Google Scholar
  12. 12.
    A. M. Il'in, Coordination of Asymptotic Expansions for Solutions to Boundary Value Problems [in Russian], Nauka, Moscow (1989).Google Scholar
  13. 13.
    A. G. Baskakov, “The Wiener theorem and asymptotic estimates for the elements of inverse matrices,” Funktsional. Anal. i Prilozhen.,24, No. 3, 64–65 (1990).Google Scholar
  14. 14.
    S. Demko, “Inverses of band matrices and local convergence of spline projection,” SIAM J. Numer. Anal.,14, 616–619 (1977).Google Scholar
  15. 15.
    C. de Boor, A Practical Guide to Splines [Russian translation], Radio i Cvyaz', Moscow (1985).Google Scholar

Copyright information

© Plenum Publishing Corporation 1993

Authors and Affiliations

  • I. A. Blatov
  • V. V. Strygin

There are no affiliations available

Personalised recommendations