Adomian decomposition method (ADM) is powerful iterative method for various kinds of nonlinear equations. Although the iterative method ADM based on Taylor expansion, it is different from the traditional Taylor series method, which requires symbolic computation of the necessary derivatives of the data functions. In the 1980’s, George Adomian introduced a new decomposition method, so called Adomian decomposition method, for solving wide class of differential, integral, integro-differential and functional equations without linearizing of the equation or without discretizing of the independent variables. Our problem differs from the classical Sturm-Liouville problems in that it contain not only end-point boundary conditions, but also two additional transmission conditions at the interior point of interaction.
Namely, we will investigate the problem with cubic nonlinearity, i.e., the Sturm-Liouville equation,
-u'' (x)+u^3 (x)=2u(x), x∈[3,4)∪(4,5]
subject to the boundary conditions
u(3)=u(5)=0
and additional transmission conditions at the interior singular point x=4, given by
u(4-0)=βu(4+0)
u' (4-0)=γu'(4+0).
Anahtar Kelimeler: Sturm-Liouville Problems, Adomian Decomposition Method, Transmission Conditions, Singular Point
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