Application of differential transform method and Adomian decomposition method for solving of one nonlinear boundary-value transmission problem

Abstract

In this study, we will found the approximate solution of one nonlinear boundary-value-transition problem by using Adomian Decomposition Method and Differential Transform Method. Namely we investigate the nonlinear differential equation,y ''(x) + y(2)(x) = lambda y(x), x is an element of[1,2)boolean OR(2,3] subject to boundary conditions y(1) = y(3) = 0 and additional transmission conditions at the interior singular point x = 2, given by y(2 - 0) = gamma(1)y(2 + 0), y'(2 - 0) = gamma(2)y'(2 + 0). We obtain that using both Adomian Decomposition Method and Differential Transform Method it is possible to express analytic solutions of nonlinear boundary-value-transmission problem in terms of series without linearization, discretization or perturbation techniques.