On the Solutions of Bratu-Type Equation via the Yang Transform Adomian Decomposition Method

In this work, the analytical solution of nonlinear Bratu-type equations is investigated using the Yang Transform Adomian Decomposition Method (YTADM). The method combines the Yang transform with the Adomian decomposition method to find the solution of a given problem in the form of rapidly convergent series. This method has been applied to several nonlinear equations with initial conditions. Adomian polynomials are used to handle the nonlinear terms in the equations. The results show that the approximate solutions obtained using the YTADM method match the exact solutions with minimum error. Thus, this method proves itself to be an efficient and accurate method of solving nonlinear differential equations.