My car battery is running down even though the alternator is working well. Please i need to what is draining the battery

For starters, it sounds like your battery can't produce enough amperage. Have it tested and replace if needed. Then see if things are better.

A bad alternator no longer charges the battery, the battery will die once it is drained. This will occur more rapidly when using equipment that runs off of the battery( lights, heater blower, windshield wipers etc.) even electronic ignition will run down a battery. Your battery just went over night the alternator may have stopped working long before. Go to an auto parts store that offers free testing to make sure it is your alternator before making repairs.
Good luck.

If it starts and runs, it's not the security. Most common things I have found to drain the battery are. The alternator(even though it is putting out the voltage), the starter, the interior lights(wiring here) and the radio (Internal problems)

change the alternator is the next step here their are no user servicable parts here ,most likely cause is a diode down causing the alternator to discharge the battery ,disconnect the alternator on the large terminal and see if the battery drains

This problem may be a drain or a bad battery or alternator.

The first thing to do before going on trying to find the system that is draining the battery would be to have the battery tested and charging system tested.

A weak battery will seem ok after the car is jumped or will barely start the car and the alternator will charge it even though the alternator is overworking due to weak battery and during the day or when car does not sit long it will seem ok. then when car sits overnight or a few days battery will weaken on its own, making it look like a drain,

so first step is battery test and alternator/charging system test.

I doubt it is the PCM, though it could be, as the voltage is regulated by the PCM. It could also be the fusible link. There is a way to test, if you have a voltmeter. With the engine running, check the voltage at the alternator terminal. It should be at least 14 volts or more. Also check it at the battery. It should be the same. If lower at the battery, replace the fusible link.
If it's the same at the battery and both are above 14 volts, the charging circuit is probably fine and the problem may be a short in the car. I can send troubleshooting steps for a short if someone is good with electric circuits.
If the voltage is lower than 14 at the alternator terminal, then either the alternator is bad or the PCM is bad, and your mechanic may be right.

Sounds like a bad alternator or Voltage regulator. Get the Haynes repair manual on your vehicle and follow the directions for removing the Alternator. take the Alternator to Auto Zone or O'Rielley''s and have it tested. If it is bad you can get a new one then and install it and solve the problem. If it test good then you will need to change the Voltage regulator.

Either something is draining the power or your alternator is not recharging your battery. Do you have a DC voltmeter? With the engine running check the voltage accross the battery it should be about 14 volts. If it's down around 12.5 volts with engine running the alternator is not working. If you determine the the alternator is working and the battery goes dead, then there is a draw on the system. It could still be the alternator though, there are diodes in the alternator, a diode acts like a one way gate for electricity. With one bad diode the alternator will still work but, when you shut the car off the alternator drains the battery back down. Something is drawing it down, without testing equipment, you'll have to take it to a shop. Something you could try, after the car has been shut off for while, an hour or more, go feel if the alternator is warm or hot, if so it's drawing the battery down. Disconnect the battery overnight so it doesn't go dead on you.

Are you leaving something plugged into the Cigarette lighter by chance as that will drain it even if nothing's charging.

You may have a faulty ground somewhere, but that will be really hard to trace as you would have to test each wire...

See if you can find someone with a multimeter and hook it up to battery, to see what voltage it reads before you try to start it, then write it down.Now boost it or whatever you have to do to get it running, and check voltage & record it with engine running. Voltage should be higher when engine running, approx 13.5 or 14 volts as compared to 12-12.5 when not running. If no increase, you have an alternator problem most likely. Let me know what you find.