  AApplying the Born-Infeld Anti de Sitter charged black hole metric we
calculate holographic entanglement entropy (HEE) by regarding the proposal of
Ryu and Takanayagi. To do so we assume that time dependence of the black hole
mass and charge to be as step function. Our work is restricted to small
subregions where a collapsing null shell dose not penetrate the black holes
horizon. To calculate time dependent HEE we use perturbation method for small
subregions where turning point is much smaller than local equilibrium point of
black hole. We choose two shape functions for entangled regions on the boundary
which are the strip and the ball regions. There is a saturation time at which
the null shell grazes the turning point and the HEE reaches to its maximum
value. In general, this work satisfies result of the works presented by Camelio
et al and Zeng et al. We must point out that they used equal time two-point
correlation functions and Wilson loops instead of the entanglement entropy (EE)
as non-local observable to study this thermalization by applying the numerical
method.
