Abstract
Perturbation iteration method has been recently constructed and it has been also proven that this technique is very effective for solving some nonlinear differential equations. In this study, we develop the new optimal perturbation iteration method based on the perturbation iteration algorithms for the approximate solutions of nonlinear differential equations of many types. This work will greatly improve the computational efficiency of the perturbation iteration method. Applications also show that only a few terms are required to get an approximate solution which is more accurate and efficient than many other methods in literature.
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