Invariant imbedding and the numerical integration of boundary-value problems for unstable linear systems of ordinary differential equations

Richard Ernest Bellman, H. H. Natsuyama, Robert E. Kalaba

ResearchPublished 1965

In such diverse areas as radiative transfer in planetary atmospheres and optimal guidance and control, two-point boundary-value problems for unstable systems arise, greatly complicating the numerical solution. This memorandum presents an invariant imbedding technique that is useful in overcoming these frequently encountered instabilities. The results of some numerical experiments are also presented. The authors show that invariant imbedding can lead to the solution of seemingly unrelated problems in other areas. 15 pp.

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  • Copyright: RAND Corporation
  • Availability: Available
  • Year: 1965
  • Print Format: Paperback
  • Paperback Pages: 15
  • Paperback Price: $20.00
  • Document Number: RM-4800-PR

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RAND Style Manual
Bellman, Richard Ernest, H. H. Natsuyama, and Robert E. Kalaba, Invariant imbedding and the numerical integration of boundary-value problems for unstable linear systems of ordinary differential equations, RAND Corporation, RM-4800-PR, 1965. As of October 11, 2024: https://www.rand.org/pubs/research_memoranda/RM4800.html
Chicago Manual of Style
Bellman, Richard Ernest, H. H. Natsuyama, and Robert E. Kalaba, Invariant imbedding and the numerical integration of boundary-value problems for unstable linear systems of ordinary differential equations. Santa Monica, CA: RAND Corporation, 1965. https://www.rand.org/pubs/research_memoranda/RM4800.html. Also available in print form.
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