Definitions:

1. Describes doing something in a stubborn, unyielding, or inflexible manner, typically in the face of reason, emotion, or persuation. ADVERB
   • He obdurately refused to admit any mistakes, even after clear evidence was presented.
2. Implies a refusal to change or soften one's stance, despite the circumstances. ADVERB
   • She obdurately stuck to her decision, despite numerous appeals from her friends.

Synonyms:

• adamantly
• firmly
• inflexibly
• obstinately
• rigidly
• stubbornly