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Zbl 1048.34009
Analytical solution of linear ordinary differential equations by differential transfer matrix method.
(English)
[J] Electron. J. Differ. Equ. 2003, Paper No. 79, 18 p., electronic only (2003). ISSN 1072-6691/e

The authors describe a new analytical method ( the differential transfer matrix method, DTMM) for finding the exact solution of a homogeneous linear ordinary differential equation of arbitrary order with variable coefficients. Except theoretical results, also same illustrative examples are presented. At the end of the article, an exact expansion of the matrix exponential for an arbitrary $2\times 2$-matrix is given. It should be noted that an analogous form was used by {\it W. Magnus} [Commun. Pure Appl Math. 7, 649--673 (1954; Zbl 0056.34102)].
MSC 2000:
*34A05 Methods of solution of ODE
34A25 Analytical theory of ODE
34A30 Linear ODE and systems

Keywords: Ordinary differential equations; differential transfer matrix method; matrix exponential

Citations: Zbl 0056.34102

Cited in: Zbl 1077.34007

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