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Definition of methodical : 1. Arranged with regard to method; disposed in a suitable manner, or in a manner to illustrate a subject, or to facilitate practical observation; as, the methodical arrangement of arguments; a methodical treatise.
2. Of or pertaining to the ancient school of physicians called methodists.
3. Proceeding with regard to method; systematic.

Synonyms:

orderly, exact, ability, methodic, order, organized

Epicurean, picky, demanding, delicate, persnickety, careful, fussy, diligent, flawless, meticulous, rigorous, precise, prudish, discriminating, finicky, exacting, punctilious, discerning, scrupulous, proper, perspicacious, squeamish, dainty, critical, correct, priggish, particular, conscientious, severe, fastidious, accurate, prim, hypercritical, mincing, literal, qualmish, choosy

meticulously, disciplined, schematic, procedural, programmatic, tactical, mannerly, mechanical, technical

stable, steady, arranged, consistent, ordered, balanced, regular, normal, efficient, systematic, harmonious, tight, uniform, symmetrical

algorithmic, statistical, computational, suppositional, valuational, algebraic, approximate, numerical, rational, systematical, mathematical, geometric, proportional, arithmetic, calculational, judgmental

Usage examples:

• He was a methodical man and had a place for each of his belongings. - "Prescott of Saskatchewan", Harold Bindloss.
• Such masses of records and monuments necessarily require methodical treatment by men of trained intelligence and of untiring industry, learned, and accurate. - "Studies in Literature and History", Sir Alfred Comyn Lyall.
• I am always methodical, I replied, slowly. - "By Wit of Woman", Arthur W. Marchmont.