On the Solutions of Nonlinear Algebraic and Transcendental Equations using Adomian Decomposition Method

Abstract

This work presents approximate analytical solutions of nonlinear algebraic and transcendental equations through direct applications of Adomian decomposition method. The reliability and efficiency of the method in solving transcendental and nonlinear algebraic equations are demonstrated through different illustrative numerical examples. The method is shown to be conceptually and computationally simple and straightforward without any ambiguity. Also, the method as applied in this study shows that it does not require the development of any other iterative scheme that could be used to find the solution to the nonlinear equations. Additionally, the method does not require finding symbolic or numerical derivatives of any given function. With the use of the Adomian decomposition method, there is no search for an auxiliary parameter for adjusting and controlling the rate and region of convergence of the solution. The method does not require finding the correct fixed point and it is free from the problem of choosing an appropriate initial approximation. Therefore, it is hoped that the present work will assist in providing accurate solutions to many practical problems in science and engineering.