  In this work we have considered the Taylor series expansion of the dynamic
scaling relation of the magnetization with respect to small initial
magnetization values in order to study the dynamic scaling behaviour of 2- and
3-dimensional Ising models. We have used the literature values of the critical
exponents and of the new dynamic exponent $x_0$ to observe the dynamic
finite-size scaling behaviour of the time evolution of the magnetization during
early stages of the Monte Carlo simulation. For 3-dimensional Ising Model we
have also presented that this method opens the possibility of calculating $z$
and $x_0$ separately. Our results show good agreement with the literature
values. Measurements done on lattices with different sizes seem to give very
good scaling.
