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Some relationships between Green's functions and invariant imbedding

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Abstract

The method of invariant imbedding has been used to resolve the solution of linear two-point boundary-value problems into contributions associated with the homogeneous equation with homogeneous boundary conditions, with inhomogeneous boundary conditions, and with an inhomogeneous source term in the equation. The relationship between the Green's function and the invariant imbedding equations is described, and it is shown that the Green's function can be determined from an initial-value problem. Several numerical examples are given which illustrate the efficacy of the initial-value algorithm.

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References

  1. Huss, R., Kagiwada, H. H., andKalaba, R. E.,Invariant Imbedding and the Numerical Determination of Green's Functions, Journal of Optimization Theory and Applications, Vol. 6, No. 6, 1970.

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Authors and Affiliations

  1. Department of Nuclear Engineering, University of Wisconsin, Madison, Wisconsin

    C. W. Maynard (Professor)

  2. Applied Mathematics Division, Sandia Laboratories, Albuquerque, New Mexico

    M. R. Scott (Research Scientist)

Authors
  1. C. W. Maynard
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  2. M. R. Scott
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Communicated byR. E. Kalaba

This work was supported by the US Atomic Energy Commission.

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Maynard, C.W., Scott, M.R. Some relationships between Green's functions and invariant imbedding. J Optim Theory Appl 12, 6–15 (1973). https://doi.org/10.1007/BF00934832

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  • DOI: https://doi.org/10.1007/BF00934832

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