Abstract Nonlinear differential equations arise in all fields of applied mathematics, physics and Engineering hence being of fundamental importance of methods to find their solutions. In the 1980’s George Adomian introduced asemi analytical technique, known as Adomian decomposition method, for solving linear and nonlinear differential equations. The purpose of this report is to employ the Adomian decomposition method (ADM) and Adomian with Taylor decomposition method (ADMT) with new useful techniques to solve Bratu’s boundary value problem by using a new integral operator.