Homotopy Analysis Method to Solve Second-Order Nonlinear Ordinary Differential Equations

Abstract

In this research, a homotopy analysis method (HAM) is used for solving second-order nonlinear ordinary differential equations (ODEs). The approximate and complex solutions of the second-order nonlinear ODEs problem were solved using Maple software. The solution easier to solve and the computational works will be reduced when using Maple software. The numerical solution that has obtained using HAM is being compared with the exact solution and also being compared with the adomian decomposition method (ADM) to determine the efficiency and accuracy of the HAM towards the exact solution. The convergence of the HAM and the absolute error is discussed further in this research. The results for the homotopy analysis method were obtained using Maple 2015. It was observed that the homotopy analysis method and the adomian decomposition method were efficient in solving second-order nonlinear ODE. However, a modified homotopy analysis method (MHAM) can be used to obtain an approximate solution close to the exact solution.