A New Treatment of the Decomposition Method for Nonclassical Boundary Value Problems

In this work, we will adapt the Adomian Decomposition Method to nonclassical boundary value problems the main feature of which is the nature of the equations and the boundary conditions imposed. Namely, the boundary conditions contains not only end points of the considered interval, but also a interior point of singularity at which given additional so-called transmission conditions, so our problem is the nonclassical once. Based on decomposition method and our own approaches a new analytical treatment is introduced for such type transmission problems. By comparision with the exact solutions we show that the Adomian decomposition method (ADM) is an efficient method for solving nonclassical Sturm-Liouville type problems under supplementary transmission conditions.