# Talk:Method of lines

Second reviewer response to revisions:

There are just a couple of changes. Firstly I think the sign of the equation third line of page 12 (or equivalently 10 lines after equation (38)) is still incorrect. the = should be replaced by =- i.e. introduce a minus sign on the rhs of this equation. The second worry is the vast amount of work that has been done on MOL but is not cited on this review. (Of course it has to be that way.) What I tried to do was to add a few more citations to balance things a little. For example the codes mentioned are all BDF codes. I suggested on page 13 to have DASSL[2s], Radau5 and MEBDFDAE[6s] for DAES. This then would include the work of Muir, Wong and Keast which has appeared recently in TOMS and various other papers and has some comprehensive references. If the authors would make these two extremely minor changes then I would be happy to recommend their work for acceptance.

- - There was some confusion as to exactly which equation had a missing minus sign. Thank you for persevering. We have now corrected this. We have also added the additional citations - GWG.

First review:

This article is very clear and well written. The only suggestion that I have is that the authors should mention that MOL has a natural advantage in solving a mathematical model of a system that consists of a combination of ODEs and PDEs. For example, this cannot be readily accomplished using MATLAB with "pdepe", nor with the finite-element package, COMSOL.

- - Thank you for this suggestion which we have taken onboard and added an extra paragraph to the end of the section entitled: "Differential Algebraic Equations" - GWG.

Second Review:
Referee's report on MOL paper by Hamdi et al.\(\ldots\)

The article is suitable for publication after the authors consider these comments.

1) page 1 halfway down the solution of time dependent partial differential...

2) page 2. \(u\) dependent variable depending on \(x\) and \(t\).

3) page 2 half way down Eq. (1) is termed the diffusion or heat equation

4) page 2 halfway down coefficient not coeffcient

5) two lines later is the partial derivative not is a partial derivative

6) two lines later derivative incorrectly spelt.

7) page 3 top. .. conditions for eq.(1) (there are several other possibilities)

8) page 3 line 3 \(u_{0}(x)\). no need to restrict the condition to a constant.

9) replace line 4 by where \(u_{0}(x)\) is a given function of \(x\).

10) page 3 line 8. .... for all t. Another very common possibility is where the initial condition is given as above and the boundary conditions are \(u(x=x_{0},t) = f_{0}\) and \(u(x=x_{f},t) = f_{b}\).

11) discuss the problem of whether we need the Bcs to be continuous i.e. do we need \(u_{b} = u_{0}(x_{0})\)

12) page 4 line 8 for example \(u_{t}\) is shorthand notation for..

13) page 4 line 10 \(u_{xx}\) represents.

14) page 5 middle that it it can be very........

15) page 6 mid page If the function depends only on the independent....

16) page 6 line -6 as it might be applied to any ....

17) two lines after equation (17) along the grid, assumed constant for the time being.

18) page 7 half way so that the solution of a system of

19) one line later approximates the solution of the original PDE

20) in equation 22. for all t .ge. 0.

21) page 8 "of order delta \(x\)". Next line remove 'to the first power'

22) the term truncation error is used in line 4 but is not defined yet

23) next line remove 'of' in the finite difference of eq. (17).

24) page 8 line 11 remains an approximation to the derivative.

25) page 10 line -2. Should also mention down winding and spend more time explaining these concepts.

26) page 12 line -16 (in the last equation on this page) a minus sign is missing after =

27)In the paragraph Sources of ODE/DAE integrators. .... for these routines. The LSODE and VODE series of ODE/DAE integrators [2s], DASSL[2s] Radau5 and MEBDFI[6s] for DAEs and the SUNDIALS.....

28) after are also available [6s]. Some very challenging test problems for ODE/DAE routines as well as some very efficient codes and an abundance of illustrative test results can be found on [6s].

- - Thank you for the considered review. The article has been updated in response to
*second review*comments: 1-7, 9, 10, 12-21, 23, 24, 27, 28. The implications of the remaining comments are still being considered - GWG.

- - We have now addressed the outstanding
*second review*comments - GWG. - * Review comments 11, 22 and 25 have now been addressed.
- * We believe that Review comment 8 has been addressed by other updates.
- * We believe that review comment 26 is either not correct or needs elaboration.

The article is suitable for publication after the authors consider these comments.

1) page 1 halfway down the solution of time dependent partial differential...

2) page 2. dependent variable depending on and .

3) page 2 half way down Eq. (1) is termed the diffusion or heat equation

4) page 2 halfway down coefficient not coeffcient

5) two lines later is the partial derivative not is a partial derivative

6) two lines later derivative incorrectly spelt.

7) page 3 top. .. conditions for eq.(1) (there are several other possibilities)

8) page 3 line 3 . no need to restrict the condition to a constant.

9) replace line 4 by where is a given function of .

10) page 3 line 8. .... for all t. Another very common possibility is where the initial condition is given as above and the boundary conditions are and .

11) discuss the problem of whether we need the Bcs to be continuous i.e. do we need

12) page 4 line 8 for example is shorthand notation for..

13) page 4 line 10 represents.

14) page 5 middle that it it can be very........

15) page 6 mid page If the function depends only on the independent....

16) page 6 line -6 as it might be applied to any ....

17) two lines after equation (17) along the grid, assumed constant for the time being.

18) page 7 half way so that the solution of a system of

19) one line later approximates the solution of the original PDE

20) in equation 22. for all t .ge. 0.

21) page 8 "of order delta ". Next line remove 'to the first power'

22) the term truncation error is used in line 4 but is not defined yet

23) next line remove 'of' in the finite difference of eq. (17).

24) page 8 line 11 remains an approximation to the derivative.

25) page 10 line -2. Should also mention down winding and spend more time explaining these concepts.

26) page 12 line -16 (in the last equation on this page) a minus sign is missing after =

27)In the paragraph Sources of ODE/DAE integrators. .... for these routines. The LSODE and VODE series of ODE/DAE integrators [2s], DASSL[2s] Radau5 and MEBDFI[6s] for DAEs and the SUNDIALS.....

28) after are also available [6s]. Some very challenging test problems for ODE/DAE routines as well as some very efficient codes and an abundance of illustrative test results can be found on [6s].

- - Thank you for the considered review. The article has been updated in response to the points raised with the exception of point 26 which we believe is either not correct or needs elaboration - GWG.

## User 4: Equation numbering

The equation numbering is not working, please see this article [[1]] --Boe 15:05, 9 January 2011 (CST)