My male cat got mature and was yowling whole day. We don't want to neuter him, so we bought a female cat approximately the same age as him. Female seems to be calm after 2 days in her new house, but our male cat has started running after her and she also runs away to save herself. Our male cat is the one starting the fight and is still yowling loudly all day. His sound pisses us off. What should be done so that they don't fight? How much time will they take to mate? They are my first pets, I don't know much about behavior of cats. Thanks.
The male sees the female cat as an invader or worse a prey. The same thing is valid for the female but the other way around. She believes she is in another cats territory so she will not attempt to fight back choosing to flee instead. As a result locking them in different rooms or allowing them to fight it out will not work as their mindset will not change.
You need to prepare a high space for the female cat so that she feels like she has a safe spot which will prevent her from fleeing and once the female cat starts viewing your house as her home rather than feeling like an invader your male cat will follow suit and won't attack her anymore.
chris bits a youtuber guy who experience this situation by bringing a new bengal cat in the same room with his cat and he make a series of videos about it , ill put the links down below , it was pretty useful experience you can learn some of the attitude when cats are meet in first time and what you should do , some of the requirement you should keep in your mind is you have to be there when you close them together until they accept each other and become a one pack ! or a couple since they are a female + male .