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Stability of Linear and Almost Linear Ordinary Differential Equation by using Matlab | ||
| Baghdad College of Economic sciences University | ||
| Article 1, Volume 0, Issue 19, 2018, Pages 367-380 | ||
| Abstract | ||
| On of the methods for studying the stability of linear and almost linear ordinary differential equations is to apply the theorms that deal with the characteristic polynomial. However, before the invention of computers, the process of finding the roots of the characterstic polynomical was a difficult task in the case of systems of higher order, therefore theorms to know the distribution of these roots without finding them were established; Hurwitz's theorem and Routh – Hurwitz theorem are two of the most utilized in this regard. In this Paper the important theorms that deal with the characteristic equation are stated, and we discuss Hurwitz's theorem and Routh _ Hurwitz theorem and we suggest a direct test instead of Hurwitz and Routh – Hurwitz theorem, as well as constructing example of higher order, where the stability is studied by using this test. | ||
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