Being a researcher in numerical mathematics myself, I think that just "financing the research" is not a sufficient argument to include your advisor as co-author. The notion of "some discussion" is very imprecise and may mean that
- the problem, the idea of the solution and the composition of the work belong to your supervisor, and your work is purely technical; or
- your supervisor checked your manuscript briefly just once and made a couple of comments regarding your English.
Without knowing the level of involvement, it is impossible to judge whether or not you should include your supervisor as co-author.
To answer this question, you may wish to read your journal's policy regarding the authorship. For example, the Elsevier
's definition of authorship reads:
Authorship should be limited to those who have made a significant contribution to the conception, design, execution, or interpretation of the reported study. All those who have made significant contributions should be listed as co-authors. Where there are others who have participated in certain substantive aspects of the research project, they should be acknowledged or listed as contributors.
Order of authors
From my shoes, it seems that many researchers in the numerical mathematics prefer to list the authors alphabetically, i.e. the order of authors does not reflect their contribution. However, when I personally publish together with researchers in applied areas (like Chemistry and Physics) in journals like Phys Rev B, we prefer to follow their convention, where the first author is the "main" author, and the last one is the one who "finance" the research. This leads to a certain amount of confusion, when all these papers appear together on your CV. Arguably, a good decision is to describe the contribution of all co-authors in a special section at the end of your paper.