Analytical proofs in mathematical papers

[marellasunny]

I am writing my first paper in applied mathematics.I would like to know how important is it to write a analytical proof for the numerical solutions arrived?I always thought these sort of things were left to the 'pure mathematicians' and one didn't need to bother.As a engineer,I was always used to substituting into formulae and arriving at solutions :). But,now that I write a paper for a journal,should I make it more theoretical?

This is what I am writing my paper on:

I am making a mathematical model of a ecological system.I use a system of non-linear differential equations to model the system.These equations involve parameters.On modelling these system of equations numerically in MATLAB ,I arrive at "surfaces with folds" i.e cusps,elliptic umbilics etc. Should I arrive at a mathematical-analytical proof to explain the reason for the shapes of these surfaces?Do I even need to for a applied math paper?

 

[Studiot]

If you wish to include such material I would suggest an appendix rather than inclusion in the main body of the text.

 

[marellasunny]

I hope I am not misleading with the term 'analytical proof'.I meant it in the pure math sense.The reason I have this doubt is because I am writing a mathematical biology paper and it wouldn't make sense to include MATLAB programs in the paper,rather a mathematical proof would give the reader a straight idea as to what the system is and how it would behave if varied.So,I ask again,would it make sense to include a mathematical proof(already in existence) and a few lines of the author's mathematical understanding of the subject in a 'mathematical biology' paper?
Thanks

 

[Stephen Tashi]

Look at other papers published in the journal you are sumitting your paper to. See what type of expositions the editors of the journal have accepted.

 

[CellCoree]

As a scientist, it is important to understand the role of analytical proofs in mathematical papers. While numerical solutions can provide valuable insights and results, they are often limited in their ability to fully explain the underlying mathematical principles and relationships at play. Analytical proofs, on the other hand, offer a more rigorous and comprehensive understanding of the problem at hand.

In the field of applied mathematics, it is common to use both numerical and analytical approaches to solving problems. While engineers may be more accustomed to using numerical methods, as a scientist it is important to recognize the value of analytical proofs in providing a deeper understanding of the results obtained.

In the case of your paper on ecological systems, it may be beneficial to include an analytical proof to explain the shapes of the surfaces you have observed. This will not only add credibility to your findings, but also provide a more complete understanding of the system you are studying. Additionally, including a theoretical aspect in your paper can enhance its overall impact and make it more relevant to a wider audience.

Ultimately, the decision to include an analytical proof in your paper should be based on the significance of the results and their potential impact on the field. While it may require more effort and time, it can greatly enhance the quality and validity of your research. As a scientist, it is important to strive for a balance between practical applications and theoretical understanding in order to advance our knowledge and understanding of the world.