Some methods for approximate solutions of the boundary-value problems

In this thesis study, to obtain the approximate solutions of boundary-value problems, Differential Transform and Adomian Decomposition methods were used. In the first part, the studies in the literature were mentioned. In the second chapter theoretical foundations were introduced. In the third part, the results were evaluated by applying some methods to linear and non-linear boundary-value problems involving transmission conditions. Whenever possible the exact and approximate solutions were compared and values on graphs and tables were examined. Using the specified methods, approximate solutions of non-linear boundary-value-transmission problems were found and compared. In addition for the nonlinear initial-value problem involving transmission conditions, approximate solution function has been demonstrated by applying the differential transformation method. Also, to find the eigenvalues of Sturm-Liouville problems, it has been shown how the Adomian decomposition method should be applied. In the last chapter, the obtained results were evaluated.