Application of differential transform method and Adomian decomposition method for solving of one nonlinear boundary-value-transmission problem - Yücel, Merve; Mukhtarov, Oktay (AIP conference proceedings, 2019)
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)+y2(x)=λy(x),x∈[1,2)∪(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) = γ1y(2 + 0), y′(2 − 0) = γ2y′(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.