Journal of Optimization Theory and Applications

, Volume 12, Issue 4, pp 344–354 | Cite as

Convergence of an initial-value method for Fredholm integral equations

  • M. A. Golberg
Article

Abstract

A convergence theorem is established for a method of solving Fredholm integral equations due to Kalabaet al. To do this, an interpolation procedure is developed for obtaining an approximation of the resolvent kernel. The results of Anselone and Moore on collectively compact operators are then applied to show convergence.

Keywords

Optimization Theory Convergence Theorem Compact Operator Discrete Version Quadrature Rule 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Casti, J. L., andKalaba, R.,On the Equivalence Between a Cauchy System and Fredholm Integral Equations, University of Southern California, Technical Report No. 70–19, 1970.Google Scholar
  2. 2.
    Golberg, M. A.,Initial Value Methods in the Theory of Fredholm Integral Equations, Journal of Optimization Theory and Applications, Vol. 9, No. 2, 1972.Google Scholar
  3. 3.
    Golberg, M. A.,Initial Value Methods in the Theory of Fredholm Integral Equations, II, Journal of Optimization Theory and Applications, Vol. 9, No. 6, 1972.Google Scholar
  4. 4.
    Anselone, P. M.,Collectively Compact Operator Approximation Theory and Applications to Integral Equations, Prentice-Hall, Englewood Cliffs, New Jersey, 1971.MATHGoogle Scholar
  5. 5.
    Hille, E.,Lectures on Ordinary Differential Equations, Addison-Wesley Publishing Company, Reading, Massachusetts, 1968.Google Scholar

Copyright information

© Plenum Publishing Corporation 1973

Authors and Affiliations

  • M. A. Golberg
    • 1
  1. 1.Department of MathematicsUniversity of NevadaLas Vegas

Personalised recommendations