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The phrase "the method presented" is correct and usable in written English
It can be used when referring to a specific method that has been introduced or discussed in a document or presentation. Example: "In this paper, we will evaluate the effectiveness of the method presented in the previous section."
Dictionary
the method presented
noun
A process by which a task is completed; a way of doing something (followed by the adposition of, to or for before the purpose of the process).
synonyms
Exact(60)
The method presented has two salient features.
We applied the method presented above to UK urban areas.
The method presented in [16] consists of two phases.
Therefore, we extended the method presented in [22].
These matrices are computed using the method presented in [9].
The method presented allows independent, two-degree-of-freedom design.
Examples are included to illustrate the method presented.
The method presented in this thesis has several advantages.
The method presented is illustrated with a numerical example.
In addition, Table 2 shows the exact and approximate solutions using the method presented in Section 3 and compares the results with the method presented in [16].
The method presented here is restricted to periodic computational domains.
More suggestions(17)
the method participated
the method incorporated
the method represented
the method preferred
the procedure presented
the method proposed
the modes presented
the approaches presented
the methods presented
the method representing
the method represents
the interaction presented
the theater presented
the assignment presented
the tape presented
the opportunity presented
the fall presented
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com