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Stability region of integration methods

Stability region of integration methods

Hi everyone,

I have a question regarding the stability of integration methods. In the following link (integration methods) is stability region in many cases written as |(a,b) Pade| < 1. I have read the provided article on Wikipedia, but I still don't know how to use provided stability region.Could someone please tell me (perhaps on Explicit Euler example) how to plot stability plot using stability region written in form of Pade table.

Best regards

Re: Stability region of integration methods

Since there was no reply to my question I figuered it out by myself. Perhaps this is going to be useful for someone else. I am going to explain it on explicit Euler example. The stability region for Euler is written as |(1,0) Padé | ≤ 1. We look at the table in Wikipedia (title: An example – the exponential function) and take the equation which is located in 1st row and 0th column ((1+z)/1). We insert some complex numbers as z and check if the absolute value of the result is smaller than 1. We then plot z on a plot with real x-axis and imaginary y-axis. The result of Euler example is shown in the attachement.
https://openmodelica.org/images/agorapro/attachments/6066/mini_stabilityEuler2.jpg

Edited by: Perun - Dec-27-17 07:52:41
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