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Projection methods and singular two point boundary value problems

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Summary

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.

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References

  1. Baxley, J. V.: Eigenvalues of singular differential operators by finite difference methods. I. J. Math. Anal. Appl.38, 244–254 (1972)

    Article  Google Scholar 

  2. de Boor, C.: The method of projections etc.... Doctoral thesis, The University of Michigan, Ann Arbor, 1966

    Google Scholar 

  3. de Boor, C.: On uniform approximation by splines. J. Approximation Theory1, 219–235 (1968)

    Article  Google Scholar 

  4. de Boor, C., Swartz, B. K.: Collection at Guassian points. Los Alamos Scientific Laboratory Report LA-DC-72-65, Los Alamos, New Mexico

  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. Dunford, N., Schwartz, J. T.: Linear operators, part II. New York: Wiley 1963

    Google Scholar 

  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. Jerome, J., Pierce, J.: On spline functions determined by singular self-adjoint differential operators. J. Approx. Theory5, 15–40 (1972)

    Google Scholar 

  9. Lucas, T. R., Reddien, G. W.: Some collocation methods for nonlinear boundary value problems. SIAM J. Numer. Anal.9, 341–356 (1972)

    Article  Google Scholar 

  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. Mikhlin, S. G.: The numerical performance of variational methods. The Netherlands: Wolters-Noordhoff 1971

    Google Scholar 

  12. Naimark, M. A.: Linear differential operators, part II. New York: Ungar 1968

    Google Scholar 

  13. Nitsche, J.: Ein Kriterium für die quasi-optimalitat des Ritzschen Verfahrens. Numer. Math.11, 346–348 (1968)

    Google Scholar 

  14. Reddien, G. W.: Some projection methods for the eigenvalue problem, to appear

  15. Russell, R. D., Shampine, L. F.: A collocation method for boundary value problems. Tech. Report 205, The University of NewMexico, Alberquerque, NewMexico

  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 

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Reddien, G.W. Projection methods and singular two point boundary value problems. Numer. Math. 21, 193–205 (1973). https://doi.org/10.1007/BF01436623

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  • DOI: https://doi.org/10.1007/BF01436623

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