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Simultaneous Approximation of Function and Derivative on [0,∞] and an Application to Initial Value Problems

  • Charles Hall
Chapter
Part of the NATO Advanced Study Institutes Series book series (ASIC, volume 49)

Abstract

Convergence of the approximation of a class of functions defined on [0,∞] and their derivatives by exponomials and Laguerre functions is established. These results are used in the analysis of a new finite element type for initial value problems.

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References

  1. 1.
    G. Birkhoff, M. Schultz and R. S. Varga, “Piecewise Hermite Interpolation in One and Two Variables with Applications to Partial Differential Equations,” Numer. Math. 11, (1968), 232–256.CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    J. C. Cavendish and C. A. Hall, “Blended Infinite Elements for Parabolic Boundary Value Problems,” General Motors Research Publication GMR-121, 1977.Google Scholar
  3. 3.
    J. C. Cavendish, C. A. Hall and 0. C. Zienkiewicz, “Blended Infinite Elements for Parabolic Boundary Value Problems,” Int. J. Num. Meth. Engg. (to appear).Google Scholar
  4. 4.
    J. C. Cavendish, C. A. Hall and T. A. Porsching, “Galerkin Approximations for Initial Value Problems with Known End Time Conditions,” submitted for publication.Google Scholar
  5. 5.
    P. J. Davis, Interpolation and Approximation, Blaisdell, London, 1963.zbMATHGoogle Scholar
  6. 6.
    J. Douglas, Jr. and T. Dupont, “Galerkin Methods for Parabolic Equations,” SIAM J. Numer. Anal. 7, (1970), 575–626.CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    P. J. Harley and A. R. Mitchell, “A Finite Element Collocation Method for the Exact Control of a Parabolic Problem,” Int. J. Num. Meth. Engg. 11, (1977), 345–353.CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    H. S. Price and R. S. Varga, “Error Bounds for Semidiscrete Galerkin Approximations of Parabolic Problems with Applications to Petroleum Reservoir Mechanics,” in Numerical Solution of Field Problems in Continuum Physics, SIAM-AMS Proc. II, AMS, 1970.Google Scholar
  9. 9.
    M. H. Stone, “A Generalized Weierstrass Approximation Theorem,” in Studies in Modern Analysis, 1, R. C. Buck, ed., MAA-Prentice-Hall, Englewood Cliffs, NJ, 1962.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1979

Authors and Affiliations

  • Charles Hall
    • 1
  1. 1.Institute for Computational Mathematics and Applications Department of Mathematics and StatisticsUniversity of PittsburghUSA

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