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Initial-value problems in potential theory

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Abstract

Potential theory characteristically leads to partial differential equations under boundary conditions. It is shown that these boundary-value problems can be converted directly into equivalent initial-value problems. These initial-value problems are shown to lead to a number of standard and nonstandard numerical procedures.

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References

  1. Bellman, R., Kagiwada, H., andKalaba, R.,Invariant Imbedding and the Numerical Integration of Boundary-Value Problems for Unstable Linear Systems of Ordinary Differential Equations, Communications of the Association for Computing Machinery, Vol. 10, No. 2, 1967.

  2. Angel, E., andKalaba, R.,A One Sweep Numerical Method for Vector-Matrix Difference Equations with Two-Point Boundary Conditions, Journal of Optimization Theory and Applications, Vol. 6, No. 5, 1970.

  3. Kagiwada, H., Kalaba, R., andSchumitzky, A.,An Initial-Value Method for Fredholm Equations, Journal of Mathematical Analysis and Applications, Vol. 19, No. 1, 1967.

  4. Bellman, R., andOsborn, H. Dynamic Programming and the Variation of Green's Functions, Journal of Mathematics and Mechanics, Vol. 7, No. 1, 1958.

  5. Bergman, S., andSchiffer, M.,Kernal Functions and Elliptic Differential Equations in Mathematical Physics, Academic Press, New York, 1953.

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  6. Angel, E.,Dynamic Programming and Linear Partial Differential Equations, Journal of Mathematical Analysis and Applications, Vol. 23, No. 3, 1968.

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Authors and Affiliations

  1. University of Southern California, Los Angeles, California

    E. Angel (Assistant Professor of Electrical Engineering), A. Jain & R. Kalaba (Visiting Professor of Electrical Engineering)

Authors
  1. E. Angel
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  2. A. Jain
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  3. R. Kalaba
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Additional information

This research was supported by the National Institutes of Health under Grants Nos. GM-16197-01 and GM-16437-01 and by the Atomic Energy Commission under Contract No. AT(11-1)-113, Project No. 19.

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Angel, E., Jain, A. & Kalaba, R. Initial-value problems in potential theory. J Optim Theory Appl 11, 274–283 (1973). https://doi.org/10.1007/BF00935196

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  • DOI: https://doi.org/10.1007/BF00935196

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