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The phrase "and then the method" is correct and usable in written English.
It can be used when describing a sequence of actions or steps in a process, particularly when introducing a specific method after discussing previous steps.
Example: "First, we gathered the necessary materials, and then the method for conducting the experiment was explained in detail."
Alternatives: "followed by the method" or "after that, the method".
Exact(21)
And then, the method has been applied to correct experimental data taken from a microscope type of Micro-CT system.
The stack trace can be read chronologically from bottom to top - that is, first the method testInsertBack was called, and then the constructor for BuggyIntDList was called, then the constructor for IntDList, and then the method insertBack was called.
The discretized equation of motion is obtained by the finite element method, and then the method of multiple scales is adopted to investigate the dynamic instability region.
To obtain the Fokker-Planck equation, slowly varying variables are replaced by their long-time averages [2] and then the method of stochastic averaging is employed [3, 4].
In the first approach, the equations are discretized first and then the method of multiple scales is applied to the resulting equations.
Boundary-value and initial-value differential equations are solved using finite difference method and graph products, and then the method is applied to the dynamic equations of modal analysis.
Similar(39)
FUUTs are assumed to be introduced in the typical metropolitan city in China, i.e., Beijing in 2012, and then the methods to predict the performance and estimate the health and economic benefits are established.
In the Prior and Posterior Analytics, Aristotle reflects first on the aims and then the methods of inquiry into nature.
The exponential stabilizability conditions are independent of the derivatives of the time-varying delays and then the methods used in [7, 12, 15, 38, 40] are not applicable to this system.
The literature search is reported first and then the methods employed in evaluating the questionnaires.
The SYK CDC25C peptide complex structure was minimized by first using the simplex method and then the Powell method to the energy gradient < 0.05 kcal/(mol·Å).
More suggestions(15)
and then the mode
and so the method
and then the methods
and after the method
and then the arrangements
and then the identified
and then the derived
and then the constructed
and then the calculated
and then the preferred
and then the used
and then the shelf
and then the action
and then the announcement
and then the place
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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