In introductions to stability analysis such as http://www.it.uu.se/edu/course/homepage/bridging/ht13/Stability_Analysis.pdf (Stability Analysis, Siyang Wang, September 26, 2013), the conclusions hold for the 'test equation' y' = lambda y, where lambda is a constant. Are there proofs for more general equations?
Dear Jad Nohra,
Look in the book Numerical Method and Meteorology: Solved Problems by Milivoj B. Gavrilov, Ivana A. Tosic and Miodrag Rancic (https://www.researchgate.net/publication/261729269_Numerical_Method_in_Meteorology_Solved_Problems)
Sincelery,
Milivoj, B. Gavrilov
Book Numerical Method in Meteorology: Solved Problems
Thank you! This is a gold mine!
Could you nevertheless point me to equations that do not fall under the umbrella of the 'test' equation? As far as I can see, both the oscillation equation and the friction equation do fall under it. Is there analysis of equations such as y'=f(y), or is it so that this form can also be reduced to the test equation?
Dear Jad,
I suggest you take a look at Chapter 7 in the book:
A.S. Ackleh, E. Allen, R.B. Kearfott, P. Seshaiyer, Numerical Analysis: Theory Methods and Practice (Graduate Textbook). Taylor and Francis Publishing, 2009.
Best,
Azmy S. Ackleh
I presume that you might have found a satisfactory answer by now, but just in case not....
The analysis in the notes from Sweden may be extended easily to higher order systems of linear ODEs. Let us take the original system to be, y'=-ay, (which has a sign change compared withe Swedish note) and therefore we require |1-ah|
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