Study of the Hypergeometric Equation via Data Driven Koopman-EDMD Theory

Round 1

Reviewer 1 Report

The topic is interesting. Perhaps the paper is written in a word document, and there are many typing mistakes, especially in mathematical expressions. For instance, see

1- page 4, In defining matrix A, and in hypergeometric equation (3.1)

On page 4, at various places, n0 is written while 0 should be written in the subscript. 

2- space are missing on page 1, 5, and some other places as well.

3- The paper should be revised, and the presentation should be improved. 

4- It is better to write the paper in Latex to avoid such discrepancies. 

5- At various places, data isn't readable, for instance eigenvalues on page 8 and 9.

 

Author Response

Reviewer 1

The paper has been written in Latex. It has been revised according to the comments of Reviewer 1.

All typing mistakes have been fixed (including those indicated by the referee).

Several mathematical data have been replaced by equations and they are not in figures.

For example,

• The matrix A and Equation (3.1) in page 4,
• Eigenvalues in pages 8 and 9

In page 4, every n0 has been replaced and has been fixed as .

 

 

Author Response File: Author Response.pdf

Reviewer 2 Report

1.      The references are not cited in the order.

2.      The symbols should be defined mathematically.

3.      Equation (3.1) is not well defined.

4.      The mathematical portion is very poor in presentation. It is pasted like a picture, not properly typed.

5.      In the graphs, colours of the lines are not clear.

 

6.      The style of the references is not uniform with the whole text.

Author Response

Reviewer 2  

• The list of references has been checked and all references are listed in order.
• The paper has been written in Latex and the presentation has been improved according to the comments of Reviewer 2. For instance, Equation (3.1) is clear now. All symbols are
• Every picture containing mathematical formulas has been deleted. All formulas have been typed.
• We have increased the resolution of the pictures.
• The references in the text have been checked and the style is now uniform with the whole text.

 

Finally, grammatical and syntax errors have been fixed accordingly.

Author Response File: Author Response.pdf

Reviewer 3 Report

 

The paper studies the hypergeometric equation by using a Koopman−EDMD−data driven approach. It is found that all the techniques and derivation are standard without any novelty, the innovation is small. Moreover, it is not written good and didn't illustrate the results good, I don't believe the paper is of sufficient quality. 

Author Response

Reviewer 3

The paper has been written in latex and the presentation has been improved according to the comments of Reviewer 3. We have increased the scientific parameters of the article,  including novelty and its  scientific contribution. The introduction has been rewritten and is much more  clear now. Moreover, the similarity rate (result was high because of our first introductory paragraphs)  has been reduced dramatically and the new similarity rate levels are now in order.

The fact that we used the method  successfully it does not guarantee  success  when applied to some other complicated dynamical systems. We have successfully addressed the major  problem of successfully applying this method  to another case. It  is the appropriate choice of  a suitable dictionary for the initiation of  the EDMD algorithm. In our case, we examined the applicability of the method to the hypergeometric equation. It is a quite challenging case   and the choice of the suitable dictionary is a tedious and cumbersome task.

 

Author Response File: Author Response.pdf

Reviewer 4 Report

1. what are  the practical applications of the method used?????

 

2.  in the bibliography enter works  from the journal!!!!!!!!!!!!

Author Response

Reviewer  4

The article has been rewritten and prepared according to the comments of Reviewer 4.

 Presentation is clear. For clarification purposes, note that the method we presented in this article applies as follows:

• To dynamical systems with unknown dynamics in order to approximate its trajectories
• to dynamical systems with known dynamics, in order to achieve better control properties.

Finally, the language fluency problem of the article has now been fixed and all necessary references are included in the paper.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

I have reviewed the revised version of the paper, and it looks good. Now, my recommendation is that the paper is accepted for publication.

Author Response

According to reviewers comment the article now looks good. 
For the convenience of the reader in the new version of our article we have added references [1], [8], and [9].

Reviewer 3 Report

I have no further comment except that all the figures are not clear, so the authors should redraw them.

Author Response

According to reviewers suggestion in the new version of our article we have redrawn all graphics which look very clear now.