I'm not a native English speaker, so I had a trouble when translating the follow sentence:
The use of an implicit operator of this form liberalizes the stability restrictions appreciably and raises the maximal permissible value of min by a factor of 2-10 over that of an explicit scheme of time advancement at typical values of the problem and grid parameters used in the simulations.
What does the over that of mean?? Could you comment please?
The "over that of" is a comparison that could be replaced with "more than" or "better than". Even as native English speaker, I had to read this sentence multiple times to understand it because of how long it is. Stripping out technical details, I've reduced the sentence to get a much easier sentence to parse.
"[This technique] raises [something] by a factor of 2 to 10 times more than [something else]"