Non-Gaussian Quadrature Integral Transform Solution of Parabolic Models with a Finite Degree of Randomness
Round 1
Reviewer 1 Report
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Comments.pdf
Author Response
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Reviewer 2 Report
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Comments for author File: Comments.pdf
Author Response
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Reviewer 3 Report
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Author Response
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Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
I have examined the revised manuscript, mathematics-850258, and reply from the authors. The authors’ answers are satisfactory. However, there is a few opinions and question for asking the authors again.
- On page 3: There is “de” appearing in the definition of the complex number i is supposed to be “of”.
- In the last Comment 7, the authors gave the reference [16, Sec. 3.1.3 Pages 276-277], but I cannot find it in the cited book of the version in 2004. Please confirm the version is 2004 or not. And, please copy the two pages for me.
Because in (37) the derivative of x is 2nd order, there need two boundary conditions for solving the problem in (37). At least, u(x, t) must be finite when x approaches infinity. Otherwise, the exact solution of u cannot be found.
In (38), what is the meaning of the argument v? It’s neither about time nor about space. What is it?
- About the last Comment 11: According to the reply to such comment from the authors, I suggest the authors adding “after taking the real part” after “… of problem (37)” on the second line on Page 9 because there is a complex number i in (43).
Author Response
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Author Response File: Author Response.pdf
Reviewer 2 Report
The article has been revised properly.
Authors have addressed my comments and the manuscript in the current form can be accepted for publication.
Author Response
We would like to thank the Reviewer the useful comments and suggestions. We feel that they have made a substantial contribution to improving the quality of the paper.
