Optimal perturbation iteration method for semi analytical solutions of different types of differential equations

This thesis consists of five chapters. The first chapter is introduction chapter. In this chapter, the place and importance of non-linear differential equations in scientific world are mentioned. In addition, general information about the proposed methods for solving these equations and some basic definitions and theorems are given. In the second chapter, the perturbation iteration method is re-examined and the basis for the construction of the optimal perturbation iteration algorithms is prepared. In the third chapter, the optimal perturbation iteration method is introduced and new algorithms are developed for both ordinary and partial differential equations. In the fourth chapter, the differential equations frequently encountered in the literature are solved with the algorithms obtained in the previous section and new approaches to these equations are found. By comparing these solutions with other methods, the effectiveness and reliability of the optimal perturbation iteration method are tested. In the fifth chapter, some suggestions are given for the methods that can be discovered by discussing the superior and missing aspects of the newly discovered optimal perturbation iteration method compared to other methods.