Talk:Stiff delay equations

The article is well written, exhaustive (at the Scholarpedia level), and pleasant to read. Also the list of available codes and bibliographic references is complete and useful for the reader interested in more deep investigation. This is my only (minor) remark: The second paragraph is entitled "Further stiff delay equations" whereas the previous one does not mention at all the presence of stiffness in the scalar and vector linear model described therein. Actually the singularly perturbed delay equation, as well as other examples in that paragraph, are just introduced as stiff equations (because of the smallness of \(\epsilon\)). On the contrary, the liner case is not stiff "in se". I think that few words could dispel the doubts in a non expert reader.

Review 2.

This is a very readable introduction to the stiffness in the context of delay differential equations. Although the relevant issues are not pursued to the complete resolution there is enough information to further explore these topics. However, this information is not always given when the issue is discussed for the first time but somewhat later. This is the case, for example, when stability of implicit Euler method, mid-point rule and the trapezoidal rule is discussed in Section on Numerical Stability of simple integrators. Some pointers to the literature would be useful here (some of the pointers are provided later). Similarly, pointers to the literature would be useful when the condition (6) is first introduced and delay-independent stability if first discussed.

Also the paper would benefit by adding additional section or paragraph when the stability for neutral delay differential equations is discussed. The reference for the scalar case is the paper by A. Bellen, Z. Jackiewicz and M. Zennaro, Stability analysis of one-step methods for neutral delay-differential eqautions, Numer. Math. 52(1988), 605-619.

Additional remark - caption to Figure 4 is missing.

Response to Review 2.

Thank you for adding additional references and paragraph on neutral equations. I noticed only two additional misprints:

1. Add comma before see Guglielmi (1998) in Section Stability domains 2. Replace Waltman by Waltman, 1978 in the last sentence before Software section

Response by the authors.

We thank both referees for their very useful remarks.