A new perturbation-iteration method and engineering applications

In this study, a new perturbation-iteration method is developed systematically for both linear and nonlinear differential equations. The proposed method is generated via classical pedestrian perturbation series and Taylor series approach. The perturbation-iteration method is classified based on the numbers of perturbation terms and Taylor series terms. In the second and third chapter, the ideas put forward in are generated mathematically for first and second order differential equations respectively. Later, the developed algorithms are applied to problems mostly used by researchers to discuss the reliability of their methods. The numerical data obtained from the perturbation-iteration solutions of the application problems was contrasted with exact solutions or numerical solutions as well as solutions of the other methods from literature. In the fourth chapter, the proposed perturbation-iteration method is generalized to first order differential equations and their systems. Application problems were compared with numerical or exact solutions.