Correct and Stable Algorithm for Numerical Solving Nonlocal Heat Conduction Problems with Not Strongly Regular Boundary Conditions

Round 1

Reviewer 1 Report

The authors present an interesting problem. Some comments:

1. The 1D heat equation (1) and the initial condition (2) are nonhomogeneous, while bothe the boundary conditions (3) are homogeneous. What does it occur if the boundary conditions are nonhomogeneous? Is the proposed scheme still valid?

2. The authors affirm that nonlocal heat conduction problems are important in solving some inverse problems. The authors should better explain this concept with reference to inverse heat conduction problems when the nonhomogeneous boundary condition is the unknown function, for example, a time-dependent heat flux.

Author Response

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Author Response File: Author Response.docx

Reviewer 2 Report

This paper presents the finite difference method for numerically solving the nonlocal heat conduction problems with not strongly regular boundary conditions. Detailed comments and suggestions are given below.

1) It should be useful to highlight the contribution of the present study. Any improvements on the finite difference method?

2) It would be better to add the limitation of the present study.

3) It would be interesting to discuss the feasibility of the present method to high-dimensional cases.

4) English should be polished in the present form.

 

 

1) It should be useful to highlight the contribution of the present study. Any improvements on the finite difference method?

4) English should be polished in the present form.

 

These two comments can be the reason for major revision.

Author Response

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Author Response File: Author Response.docx

Reviewer 3 Report

Please see the attached file. 

Comments for author File: Comments.pdf

Author Response

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Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

It can be accepted.