Fundamental matrix and two-point boundary-value problems |
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Authors: | S M Roberts J S Shipman |
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Institution: | (1) IBM Scientific Center, Palo Alto, California;(2) IBM, Federal Systems Division, Gaithersburg, Maryland |
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Abstract: | Theoretically, the solution of all linear ordinary differential equation problems, whether initial-value or two-point boundary-value problems, can be expressed in terms of the fundamental matrix. The examination of well-known two-point boundary-value methods discloses, however, the absence of the fundamental matrix in the development of the techniques and in their applications. This paper reveals that the fundamental matrix is indeed present in these techniques, although its presence is latent and appears in various guises. |
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Keywords: | Fundamental matrix invariant imbedding method of adjoints method of complementary functions method of particular solutions two-point boundary-value problems |
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