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I am writing a piece on integration of differential equations. One of the words that I have to use frequently is "timestep" (however it is written), i.e. a step forward in the "simulated" time.
There seem to be three variants:
The wikipedia article one Verlet integration in fact uses all three (!) of these variants.
Is there a context in which one is preferred over the other? How do I decide which one to use?
A general remark on hyphens from Longman English Grammar by Aleander
1 There are no precise rules.
2 When short nouns are joined together, they form one word without a hyphen (a teacup). But this may lead to problems of recognition, therefore bus stop, not busstop.
3 Hyphens are often used for verb + particle combinations as in make-up.
4 When a compound is accepted as a single word, i.e. it has an entry in a dictionary, the tendency is to write it as one word (sunbathing).
5 In other cases the use of the hyphen is at the discretion of the writer, writing paper or writing-paper.
6 But the tendency is to avoid hyphens where possible.
When I google "derivative timestep," I get many entries for "time step," but I don't get any with "timestep" on the first page. I do get "time-step," once.
Googling "derivative timestamp" gives a different set of pages, which are not about calculus but about web forum management and such (checking timestamps on posts that are "derivative"). This confirms what I know about the word "timestamp":
a sequence of characters or encoded information identifying when a certain event occurred, usually giving date and time of day, sometimes accurate to a small fraction of a second" (Wikipedia).
A timestamp marks when something happened; a time step is the interval between two times.
So I would use "time step" (because it's most common) or possible "time-step," and consider "timestep" to be an error.
As I was writing this reply, the spellchecker flags timestep as not a word, so based on that I'd avoid it. Whether you need the hyphen or not depends on your usage. If you're using it as a compound adjective, it needs a hyphen; e.x. time-step methods for solving differential equations. The words time and step describe the method together so you hyphenate. If you're using it to describe a discreet interval of time, it does not; e.x. the first time step uses a forward difference, while subsequent time steps use the central difference method. Google "compound adjectives" for more explanation.
In a course in academic writing in English, we were advised to check how popular different spellings are. For this word, I get the following result for Google Scholar.
Time step: 1 870 000 results (includes time-step)
Timestep: 126 000 results
Conclusion? Time step (or time-step) is a much more popular spelling among researchers than timestep.
Note that Google scholar makes the same search independent on whether you write "time step" or "time-step". On the first few result pages, they are equally distributed.
