Numerische Mathematik

, Volume 21, Issue 3, pp 193–205 | Cite as

Projection methods and singular two point boundary value problems

  • G. W. Reddien


The use of collocation methods and singular splines applied to singular two point boundary value problems is studied. Existence, uniqueness and convergence rates are obtained.


Convergence Rate Mathematical Method Point Boundary Projection Method Collocation Method 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Baxley, J. V.: Eigenvalues of singular differential operators by finite difference methods. I. J. Math. Anal. Appl.38, 244–254 (1972)CrossRefGoogle Scholar
  2. 2.
    de Boor, C.: The method of projections etc.... Doctoral thesis, The University of Michigan, Ann Arbor, 1966Google Scholar
  3. 3.
    de Boor, C.: On uniform approximation by splines. J. Approximation Theory1, 219–235 (1968)CrossRefGoogle Scholar
  4. 4.
    de Boor, C., Swartz, B. K.: Collection at Guassian points. Los Alamos Scientific Laboratory Report LA-DC-72-65, Los Alamos, New MexicoGoogle Scholar
  5. 5.
    Ciarlet, P. G., Natterer, F., Varga, R. S.: Numerical methods of highorder accuracy for singular boundary value problems. Numer. Math.15, 87–99 (1970)Google Scholar
  6. 6.
    Dunford, N., Schwartz, J. T.: Linear operators, part II. New York: Wiley 1963Google Scholar
  7. 7.
    Jamet, P.: On the convergence of finite difference approximations to one-dimensional singular boundary value problems. Numer. Math.14, 87–99 (1970)Google Scholar
  8. 8.
    Jerome, J., Pierce, J.: On spline functions determined by singular self-adjoint differential operators. J. Approx. Theory5, 15–40 (1972)Google Scholar
  9. 9.
    Lucas, T. R., Reddien, G. W.: Some collocation methods for nonlinear boundary value problems. SIAM J. Numer. Anal.9, 341–356 (1972)CrossRefGoogle Scholar
  10. 10.
    Lucas, T. R., Reddien, G. W.: A high order projection method for nonlinear two point boundary value problems. Numer. Math.20, 257–270 (1973)Google Scholar
  11. 11.
    Mikhlin, S. G.: The numerical performance of variational methods. The Netherlands: Wolters-Noordhoff 1971Google Scholar
  12. 12.
    Naimark, M. A.: Linear differential operators, part II. New York: Ungar 1968Google Scholar
  13. 13.
    Nitsche, J.: Ein Kriterium für die quasi-optimalitat des Ritzschen Verfahrens. Numer. Math.11, 346–348 (1968)Google Scholar
  14. 14.
    Reddien, G. W.: Some projection methods for the eigenvalue problem, to appearGoogle Scholar
  15. 15.
    Russell, R. D., Shampine, L. F.: A collocation method for boundary value problems. Tech. Report 205, The University of NewMexico, Alberquerque, NewMexicoGoogle Scholar
  16. 16.
    Vainikko, G. M.: Galerkin's perturbation method and the general theory of approximate methods for nonlinear equations. U.S.S.R. Comp. Math. and Math. Phys.7, 1–41 (1967)Google Scholar

Copyright information

© Springer-Verlag 1973

Authors and Affiliations

  • G. W. Reddien
    • 1
  1. 1.Department of MathematicsVanderbilt UniversityNashvilleUSA

Personalised recommendations