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

• Published in: AIP conference proceedings Vol. 2183; no. 1
• Main Authors: Yücel, Merve, Mukhtarov, Oktay
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Melville American Institute of Physics 06.12.2019
• Subjects: Boundary conditions; Boundary value problems; Cybernetics; Decomposition; Exact solutions; Mathematical analysis; Nonlinear analysis; Nonlinear differential equations; Perturbation methods
• ISSN: 0094-243X; 1551-7616
• DOI: 10.1063/1.5136211

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.