I would like to know if there is a qualitative difference between the phrases "high-order" and "higher-order". I have recently received a response to an article I submitted in the field of numerical methods for curvature computation of liquid-gas interfaces. In the article, I develop an arbitrary-order polynomial fitting procedure to reconstruct the liquid-gas interface, after which the interface curvature is computed (for surface tension computation purposes). I titled the article "A Higher-order Accurate ..." because I manage to demonstrate that the "order of accuracy" of the procedure matches the order of the fitted polynomial.
One of the reviewers of the article strongly suggests replacing "higher-order" with "high-order". I partially understand this request as I have noticed a trend where a number of researchers in my field use the phrase "high-order" in similar contexts to mine (although most still use "higher-order"). However, I gravitate towards "higher-order" as it is widely used all over mathematics. Can anyone advise me on the differences (if any) between these two phrases, and which one I should adopt?
I have found it difficult to settle language issues without face to face communication, something which is not possible here. It may be possible to avoid the issue entirely and still attract the right audience. Consider the title "Methods of arbitrary order for approximating <something relevant>." In the abstract, write something along the lines of : "Given an positive integer $p$ we show how to generate approximations of order $p$ for <something relevant>".