Solving linear homogeneous one-dimensional wave equation using Adomian decomposition method / Zafirah Husna Zali and Ummi Nur Umaierah Jismadi - Zali, Zafirah Husna; Jismadi, Ummi Nur Umaierah (2022)
In this paper, the linear homogeneous one-dimensional wave equation is solved using different approaches which are d’Alembert’s formula and Adomian Decomposition Method (ADM). The purpose of using different methods is to test the efficiency and accuracy of the Adomian decomposition method in solving the linear homogeneous one-dimensional wave equation. The analytical value and numerical value are obtained by applying d’Alembert’s formula and Adomian decomposition method respectively. The Dirichlet problem was chosen, as well as a variation of initial conditions for the linear homogeneous one-dimensional wave equation. Several examples have been provided to illustrate the graphical plots and numerical results. The numerical solution is derived by considering only the first four terms of the decom position. All graphical plots are computed by using Maple 2015 software while absolute error between both methods is calculated by using Microsoft Excel. The error will reflect how well the ADM performs in getting high precision approximation answers. As for the results, there is no difference between both methods since it is proven that the absolute errors for all examples are equal to zero. Hence, ADM has high accuracy and can obtain the closed solution to the analytical value efficiently.