Shraddha literally means that which is done with all faith, devotion and sincerity. That is why it is classified as a yagya. An action will be qualified to be called as yagya only if has been prescribed by Vedas and is carried out in all faith. Such a yagya will certainly bear fruit is what Vedas say.
Shraddha is a Naimiththika karma, meaning, it is obligatorily done on particular occasions. It also gets classified as Pitru yagyam. Looking after the parents during their life time is also a yagya within the same classification and it is the first part of yagya towards the parents.
The reason for prescription of yagyas is for purification of mind, which qualifies a person as eligible to progress into higher strata of pursuit of knowledge towards permanent liberation from the mundane world of endless birth and death cycles.
With the above in the background, if we look at the question, "what is the use of feeling after her death when he does not cared her while she was alive?"
It is clear that a person who has not taken care of the parents when they are alive already lacks faith and devotion and has not performed the first part of the yagya. Therefore, even if he attempts the second part of Pitr yagya, viz., it will have two defects- (1) lack of Shraddha or faith, devotion and sincerity and (2) incomplete without the first part. Therefore, the performance will not fetch him the results.
(I am not talking about a person who performs the Shraddha after realising his folly of not taking care of the parents and regretting for that and therefore performs at least the second part vlz., performance of Shraddha).
The next question that arises naturally whether the pitrus accept their son's rituals:
As regards the receipt of oblations, it is obviously symbolic and there is no expectation from the late parents that their children should offer them oblations. Moreover, the pitrs might have taken either rebirth or liberated. But the doer does not know what happened to them and he has to perform them. Why? That is the System that is in existence and one have to have faith in a System is what the elders say.
These karmas, as already stated, are for creation of a bent of mind towards gratitude and love and thus for conditioning and purification of mind, which is otherwise erratic. By nurturing gratitude to the parents who sacrificed their life for the welfare of the children, the mind will keep it in memory and the tradition will pass on to generations.
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Any details available in vedic dharma (I am avoiding the word hindu as I don't accept such a name which has not been spelt out so by Shastras) shashtras about this? or what shashtras say om this?
Yes the Shastras prescribe the performance of Shraddha undoubtedly. This is one of the pitr yagyas falling within the category of Naimiththika karma and has to be performed. Even Lord Krishna has said in Chapter XVII of Bhagavatgeeta, that there is no point in doing a karma in accordance with what Shastras have prescribed as niyata karma. The objective is already explained.