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Defect Corrections and Hartree-Fock Method

  • K. Böhmer
  • W. Gross
  • B. Schmitt
  • R. Schwarz
Part of the Computing Supplementum book series (COMPUTING, volume 5)

Abstract

In the context of Hartree-Fock methods for the Schrödinger equation a special class of EVPs for ODEs on infinite intervals is shown to play a crucial role in the computation time. The usual discretization is combined with two very efficient ways to choose the finite boundary conditions. Then two kinds of defect corrections are applied.

Keywords

Schrodinger Equation Outer Point Additional Boundary Condition Infinite Interval Defect Correction 
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References

  1. [1]
    Böhmer, K.: Discrete Newton methods and iterated defect corrections. Numer. Math. 37, 167–192 (1981).MathSciNetMATHCrossRefGoogle Scholar
  2. [2]
    Böhmer, K., Gross, W.: Hartree-Fock methods — A realization of variational methods in computing energy levels in atoms. In: Numerical Treatment of Eigenvalue Problems (Albrecht, J., Collatz, L., Veite, W., eds.). (ISNM 69.) Basel-Boston-Stuttgart: Birkhäuser 1984.Google Scholar
  3. [3]
    Froese-Fischer, Ch.: The Hartree-Fock Method for Atoms. New York-London-Sydney-Toronto: Wiley 1977.Google Scholar
  4. [4]
    de Hoog, F., Weiß, R.: An approximation theory for boundary value problems on infinite intervals. Computing 24, 227–239 (1980).MathSciNetMATHCrossRefGoogle Scholar
  5. [5]
    Jordan, Ch.: Calculus of Finite Differences, 3rd ed. New York: Chelsea Publ. Co. 1965.MATHGoogle Scholar
  6. [6]
    Keller, H. B., Pereyra, V.: Symbolic generation of finite difference formulas. Math. Comp. 32, 955–971 (1978).MathSciNetMATHCrossRefGoogle Scholar
  7. [7]
    Lentini, M.: Keller, H. B.: Boundary value problems on semi-infinite intervals and their numerical solution. SIAM J. Numer. Anal. 17, 577–604 (1980).MathSciNetMATHCrossRefGoogle Scholar
  8. [8]
    Stetter, H. J.: The defect correction principle and discretization methods. Numer. Math. 29, 425–443 (1978).MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • K. Böhmer
    • 1
  • W. Gross
    • 1
  • B. Schmitt
    • 1
  • R. Schwarz
    • 1
  1. 1.Fachbereich MathematikPhilipps-UniversitätMarburgFederal Republic of Germany

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