After updating your database table, if you are not accessing same data in this program then use UPDATE function module to finish your task.
Create one function module and pass your local internal table to that FM via tables or exporting parameter. Now LOOP your data inside the update function module and update the table. Call your UPDATE function module like below in program:
call function 'ZUPDATE_MY_TABLE' in update task
tables
Int_Tab = Int_Tab.
This will be executed as asynchronous task and you can see this update process in SM13 transaction code.
Regards,
Naveen