【Orderly】 ,  【methodical】 ,  【systematic】 ,  【regular】  are comparable when they mean following closely a set arrangement, design, or pattern.

【Orderly】 implies observance of due sequence or proper arrangement especially in the harmonious or careful disposition of persons or things or in obedience to the rules of conduct or behavior that guide disciplined persons or in keeping a place free from litter or confusion or in a scheme or system when all details stand in their proper relations, each playing its due part without interfering with that of any of the others.

【Methodical】 implies the observance of an order that has been carefully worked out so that the steps to be followed are exactly known or the pattern that is accepted seems logical or inevitable under the circumstances.

【Systematic】  comes close to  【methodical】 in ordinary use, but  【systematic】 , which always retains some notion of the ordered complex unity implied by the related noun (compare SYSTEM ), may be preferred when the stress is not upon the order followed but upon the integrated and ordered whole involved; thus,  【methodical】  study implies study pursued in 【regular】 increments according to a predetermined schedule while  【systematic】 study implies study pursued according to a scheme in which each increment leads logically to the next and the end result is exposure to an integrated block of information.

【Systematic】  also may be used to suggest order in occurrence, in progression, and especially in repetition, still with some notion of an underlying system; thus, a  【systematic】 error is one that is inherent in a system of measurement or calculation and recurs whenever that system is used.

【Regular】 , with its basic implication of conformance to a rule (see also  【REGULAR】 1 ), may come very close to  【orderly】 . The term may imply steadiness or uniformity (as in following a schedule) or it may suggest occurrence and recurrence (as at fixed or stated intervals or in uniform amount).