Manipulative Derivation of some Equations of Invariant Imbedding
Two transformations are established which convert a linear nonhomogeneous system S of ordinary first-order differential equations into a system R comprising a matrix Riccati equation and a linear nonhomogeneous ordinary matrix differential equation. If the boundary values of system 5 are two-point, then under certain conditions the solution of system R is uniquely determined by one-point boundary values. In the case when the system S is homogeneous and with boundary values evenly distributed over the two boundaries, the resulting initial value problem is identical to that of invariant imbedding, with the transformed variables retaining their classical meaning. The transformations are generalizations to large-order nonhomogeneous systems of the wide class of transformations which convert linear homogeneous second-order systems to scalar Riccati equations. A simple third-order system with two-point boundary conditions is solved for illustrative purposes.
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| Work Title | Manipulative Derivation of some Equations of Invariant Imbedding |
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| Subtitle | Astronomical Journal, 69, 560, 1964 |
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| License | CC BY-NC-SA 4.0 (Attribution-NonCommercial-ShareAlike) |
| Work Type | Presentation |
| Publication Date | 1964 |
| Deposited | March 21, 2025 |