Talk:General linear methods
<review>message to curators</review>
The article is interesting and gives a good summary of General Linear Methods. In the formula for \(M(z)\), matrix \(U\) was missing.
To make the page more self-contained I have tried to add some definitions for region of absolute stability, A-stability and L-stability.
In order to make this article easier to edit and add to in the future, I recommend that the following changes be made:
1) The discussion on DIMSIMs should be self contained and in its "own" section, rather than sprinkled throughout the text. DIMSIMs are the most researched class and therefore rightly deserve a large portion of the text. However, this would allow someone who wanted to add a section on say two-step Runge--Kutta methods to do so without affecting any other part of the text and being able to reference the first section on the theory of GLMs as a whole.
2) The first section should contain the theory and history of GLMs independent of any initial assumptions about the method. In particular I would include the Absolute stabilty properties and Classification of GLMS discussion before introducing DIMSIMs.
3) DIMSIMs and GLMS with inherent Runge--Kutta stability can then be treated as examples of GLMs and treated independently.
4) The article of J. C. Butcher on General linear methods published by Acta Numerica in 2006 should certainly be referenced.
I have modified and reaaranged the paper trying to accomodate the comments of the referee. I also added additional reference to the review paper by J.C. Butcher, General linear methods, Acta Numerica 15(2006), 157-256.
I suggest only one further change, that is to remove from "In the remainder of the paper we will restrict ... multistage integration methods (DIMSIMs)." And replace in the DIMSIMs section. This will require small tidying up of the related sentences.
I am not sure if I understand the suggested change. Trying to address the suggestion of the reviewer I just added one additional section "Diagonally Implicit Multistege Integration Methods" before "In the remainder ...".
Thanks to the author for making the appropriate changes
I am not sure if additional changes are required. I believe I already made all the requred changes and there is still a message that the reviewer is waiting for my response. What additional changes are suggested?