"methodical description" is correct and usable in written English.
You can use it to refer to an organized, step-by-step explanation of something. For example, "John gave me a methodical description of how to use the new printer."
His was the first methodical description of foundry practice.
William Langewiesche begins "The Atomic Bazaar" with a reference to Hiroshima and a chilling, methodical description of exactly how a nuclear blast destroys a city.
A variety of treatment options will achieve this end; Dr. Melman and his co-author, Rosemary Newnham, a medical writer, deliver a detailed, straightforward and methodical description of them all.
Guigo II's book The Ladder of Monks is considered the first description of methodical prayer in the western mystical tradition.
Kann, whose first book this is, relates the flower-filled affluence and heartache of her youth, but her descriptions are methodical rather than illuminating.
That Plato, appearances notwithstanding, is not indulging in a god-besotted rêverie is indicated by the interweaving of the mythical description with an emphasis on methodical 'taxonomical' procedure.
The Times article peppered a description of the match with observations of Ashe's methodical manner: On the changeovers Ashe sat still, eyes closed, meditating, relaxing for the task ahead.
Several subjects recounted more methodical means of encouraging good fortune, whether happy accidents of any description came their way.
Make the methods for identifying specific genes more explicitly methodical.
The approach is composed of several methodical steps that comprise the building of multiple scenarios, a scenario-specific analysis of the target market and customers, a description of distinct Concepts of Operations, and eventually a derivation of design requirements to form the aircraft specification.
