battery charger by using 555ic and 7815 ic with auto cut off

The charger consists of two stages: The first is a capacitive voltage doubler, which uses a 555 timer IC driving a pair of transistors connected as emitter followers, which in turn drive the voltage doubler proper. The doubler has power resistors built in, which limit the charging current.
The second stage is a voltage regulator, using a 7815 regulator IC. Its output is applied to the battery via a diode, which prevents reverse current and also lowers the voltage a bit. The resulting charge voltage is about 14.4V, which is fine for charging a gelled or AGM battery to full charge, but is too high as a trickle charger, so don’t leave this charger permanently connected to a battery. If you would like to do just that, then add a second diode in series with D3!
There is a LED connected as a charge indicator. It will light when the charge current is higher than about 150mA. The maximum charge current will be roughly 400mA.