Manifesting, exercising, or favoring rigor; allowing no abatement or mitigation; scrupulously accurate; exact; strict; severe; relentless; as, a rigorous officer of justice; a rigorous execution of law; a rigorous definition or demonstration.
source: Webster 1913
rigidly accurate; allowing no deviation from a standard
Rigorous application of the law. A strict vegetarian.
source: WordNet 3.0
demanding strict attention to rules and procedures