A new approximate method for solving linear and non- linear differential equation systems

Abstract

In this work, a new approximate method is proposed to enhance the accuracy and convergence of solutions for differential equations. This method uses the Taylors’ series in its derivation. The proposed method has used for solving different types of linear and nonlinear differential equation systems with the initial conditions. Four examples have presented to check the effectiveness, accuracy, and convergence of the method. The solutions of the proposed method also compared with those obtained by the Adomian decomposition method (ADM), and the Homotopy analysis method (HAM). The results of the proposed method outperformed the other methods in terms of accuracy and convergence.