Application of Differential Transform Method and Adomian Decomposition Method for Solving of one Nonlinear Boundary-Value-Transmission Problem

摘要

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) = λy(x), x ∈ [1,2) ∪ (2,3] subject to boundary conditions y(l) = y(3) = 0 and additional transmission conditions at the interior singular point x = 2, given by y(2 - 0) = γ_1y(2 + 0), y'(2 - 0) = γ_2y'(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.