Abstract

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.