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The phrase "and implemented the method" is correct and usable in written English.
You can use it when describing the action of putting a specific method into practice, often in a technical or academic context.
Example: "After conducting the research, the team developed a new algorithm and implemented the method to improve efficiency."
Alternatives: "and executed the method" or "and applied the method".
Exact(17)
Here, we selected the multi-kernel function and implemented the method in the R package BGLR.
Prins et al. [20] adapted three kinds of dithering modulations, which can improve the robustness of the QIM method, to the fingerprinting scheme, and implemented the method using a sufficiently large scaling factor.
The group led by M. Caruthers took the advantage of less aggressive and more selective 1H-tetrazolidophosphites and implemented the method on solid phase.
MDRC conceived and implemented the method.
LC constructed and implemented the method and performed simulation experiments.
CW and FB conceived and implemented the method.
Similar(43)
KS developed and implemented the methods.
MH developed and implemented the methods.
RW developed and implemented the methods and drafted the manuscript.
MAGB designed and implemented the methods and processed results.
SMP and DMR developed and implemented the methods.
More suggestions(1)
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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