An optimized decomposition method for nonlinear ordinary and partial differential equations

In this paper, firstly, an innovative decomposition method, called the optimized decomposition method, is suggested to analytically solve nonlinear ODEs. The proposed technique designs a new optimal construction of the series solutions based on a linear approximation of the nonlinear equation. Then, an efficient adaptation of the optimized decomposition method that will expand the application of the method to nonlinear PDEs is developed. Actual comparison between the suggested method and the Adomian decomposition method is carried out through numerical simulation of some test problems. The study demonstrates that the proposed method works successfully in dealing with nonlinear differential equations and gives better accuracy and convergence compared to Adomian decomposition method. The new proposed method reported in this work is believed to be implemented more widely to handle nonlinear models in applied sciences. (C) 2019 Elsevier B.V. All rights reserved.