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

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

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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.

This report is part of the RAND Corporation Research memorandum series. The Research Memorandum was a product of the RAND Corporation from 1948 to 1973 that represented working papers meant to report current results of RAND research to appropriate audiences.

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