A new alternative homotopy method for the approximate solution of differential equations and comparison with other methods

In this study, a new method for the approximate solution of ordinary and partial differential equations called "Alternative Homotopy Method" is introduced and applied to some problems. This method is compared with Homotopy Perturbation Method (HPM), which is commonly used in the literature. In the first section, the aim of the thesis, literature summary and the general definitions are given. In the second section, the concept of homotopy and perturbation theory are given briefly, then the Homotopy Perturbation Method is analyzed. In the third section, a new Alternative Homotopy Method is introduced. To make the work more valuable we established some existence and convergence theorems. In the fourth section, the difficulties related to regular and singular problems are examined separately. Then we demonstrated the ways to overcome these difficulties. In the fifth section, the problems containing higher order equations are discussed. The approximate series solutions for partial differential equations, considered in the sixth section. The last section, consists of some analysis and conclusions.