Application of adomian decomposition method to elliptic boundary value problems

In this thesis, the boundary value problem and elliptic inverse problem of elliptic partial differential equations are investigated using the Adomian decomposition method and their solutions are obtained. This thesis consists of five chapters. In the first section, studies on Adomian decomposition method, elliptic partial differential equations (Laplace, Poisson), well-positioned problems and Taylor series are explained. In the second section, the Adomian decomposition method is introduced. The use of the Adomian decomposition method and two sample Adomian serial solutions and their approximate solutions are given. In the third section, Adomian polynomials are shown. In this section, the calculation of Adomian polynomials with the Adomian method, the calculation of Adomian polynomials using parameters, the calculation of Adomian polynomials with the generalized Taylor series and the calculation of Adomian polynomials with the homotopy perturbation method are given. In the fourth section, the studies on the elliptic partial differential equations of the Adomian decomposition method are given. The solution of the elliptic partial differential equation and the solution of the nonlinear elliptic partial differential equation with the Adomian decomposition method are shown with an example. In the fifth section, Adomian decomposition method in elliptic inverse problems is given. Under this title, the inverse problem is introduced, the third-order partial differential equations are given, and the solution of the elliptic inverse problem is given by the Adomian decomposition method. In the sixth section, the results of this thesis study are given below.