Rigorous, a.
Etymology: [F. rigoureux, LL. rigorosus. See Rigor.]
1. 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. He shall be thrown down the Tarpeian Rock With rigorous hands. Shak. We do not connect the scattered phenomena into their rigorous unity. De Quincey.
2. Severe; intense; inclement; as, a rigorous winter.
3. Violent. [Obs.] "Rigorous uproar." Spenser.
Syn. -- Rigid; inflexible; unyielding; stiff; severe; austere; stern; harsh; strict; exact. -- Rig"or*ous*ly, adv. -- Rig"or*ous*ness, n.
Shades of meaning
Fernald has no entry of its own for rigorous; he lists it under severe.
Where he writes about it:
Rigorous is nearly akin to rigid, but is a stronger word, having reference to action or active qualities, as rigid does to state or character; a rigid rule may be rigorously enforced. — from severe
We speak of austere morality, rigid rules, rigorous discipline, stern commands, severe punishment, harsh speech or a harsh voice, hard requirements, strict injunctions, and strict obedience. — from severe
Strict discipline holds one exactly and unflinchingly to the rule; rigorous discipline punishes severely any infraction of it. — from severe