In the present research, an advanced decomposition technique based on
the Adomian decomposition method is proposed to achieve the highly
accurate numerical solution of non-linear initial value problems of
Bratu's-type without any linearization, perturbation and discretization.
For the completeness of the proposed technique, convergence analysis is
also addressed. The reliability, generality and validity of the proposed
technique are examined by calculating the absolute errors of some
initial value problems of Bratu's type. Moreover, the obtained solutions
are compared graphically with the precise solution and also with some
existing approaches solutions.