Solutions of nonlinear real world problems by a new analytical technique

Abstract

Here a new analytical scheme is presented to solve nonlinear boundary value problems (BVPs) of higher order occurring in nonlinear phenomena. This method is called second alternative of Optimal Homotopy Asymptotic Method. It converts a complex nonlinear problem into zeroth order and first order problem. A homotopy and auxiliary functions which are consisted of unknown convergence controlling parameters are used in this technique. The unknown parameters are determined by minimizing the residual. Many methods are used to determine these parameters. Here Galerkin's method is used for this purpose. It is applied to solve non-linear BVPs of order four, five, six, and seven. The Consequences are compared with other methods e.g., Differential Transform Method (DTM), Adomain Decomposition Method (ADM), Variational Iteration Method (VIM), and Optimal Homotopy Asymptotic Method (OHAM). It gives efficient and accurate first-order approximate solution. The achieved results are compared with the exact solutions as well as with other methods to authenticate the applied technique. This method is very simple and easy but more operative. � 2018 The Authors