A Hybrid Yang Transform Adomian Decomposition Method for Solving Burger’s Equation

Abstract

In this work, we obtain an approximate analytical solution of the Burgers equation by employing the Yang Transform in combination with the Adomian Decomposition Method (ADM). The Yang Transform is first used to convert the original time-dependent nonlinear PDE into a simpler form. The nonlinear convection term is then decomposed using Adomian polynomials, enabling us to construct the solution as an infinite series. Applying the inverse Yang Transform yields the approximate solution in the physical time domain. The convergence of the resulting series is examined to confirm the reliability of the method. A comparison between the approximate and exact solutions demonstrates excellent agreement. To further illustrate the dynamics of the solution, 2D and 3D plots are provided. Overall, the proposed approach is straightforward, efficient, and capable of producing solutions that closely match the exact behaviour of the Burger’s equation.