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An initial-value method for the determination of Green's functions

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Abstract

The convergence of an initial-value method for computing the Green's function of a class of second-order differential operators is established. The proof relies on an interpolation procedure which is shown to generalize the Nyström method for Fredholm integral equations. The approximate Green's function is related to the solution of a discrete summation equation. The results of Anselone and Moore on collectively compact operators are then applied.

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References

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Additional Bibliography

  1. Casti, J. L., andKalaba, R. E.,On the Equivalence Between a Cauchy System and Fredholm Integral Equations, University of Southern California, Technical Report No. 70–19, 1970.

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  3. Golberg, M. A.,An Initial Value Method for the Calculation of the Characteristic Values and Characteristic Functions of an Integral Operator, Journal of Mathematical Analysis and Applications (to appear).

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Authors and Affiliations

  1. Mathematics Department, University of Nevada at Las Vegas, Las Vegas, Nevada

    M. A. Golberg (Associate Professor of Mathematics)

Authors
  1. M. A. Golberg
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Communicated by R. E. Kalaba

This research was partially supported by UNLV Grant No. 001-060-4573.

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Golberg, M.A. An initial-value method for the determination of Green's functions. J Optim Theory Appl 11, 506–516 (1973). https://doi.org/10.1007/BF00935663

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